[{"article_type":"original","publisher":"Institute of Mathematical Statistics","page":"1623-1662","quality_controlled":"1","ec_funded":1,"title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","intvolume":"        34","publication_status":"published","date_created":"2024-02-25T23:00:56Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"b0cc634c-d549-11ee-96c8-87338c7ad808","orcid":"0000-0003-2625-495X","full_name":"McKenna, Benjamin","first_name":"Benjamin","last_name":"McKenna"}],"issue":"1B","_id":"15025","scopus_import":"1","volume":34,"acknowledgement":"The first author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by Fulbright Austria and the Austrian Marshall Plan Foundation.","abstract":[{"lang":"eng","text":"We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble."}],"doi":"10.1214/23-AAP2000","arxiv":1,"day":"01","external_id":{"arxiv":["2208.12206"]},"date_updated":"2024-02-27T08:29:05Z","citation":{"short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.","mla":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>.","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","ama":"Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. 2024;34(1B):1623-1662. doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>","apa":"Erdös, L., &#38; McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>","ieee":"L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” <i>Annals of Applied Probability</i>, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.","chicago":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>."},"year":"2024","language":[{"iso":"eng"}],"month":"02","oa_version":"Preprint","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"publication":"Annals of Applied Probability","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2208.12206"}],"oa":1,"publication_identifier":{"issn":["1050-5164"]},"date_published":"2024-02-01T00:00:00Z","type":"journal_article"},{"article_type":"original","publisher":"Cambridge University Press","file_date_updated":"2023-09-20T11:09:35Z","ec_funded":1,"quality_controlled":"1","intvolume":"        11","title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","department":[{"_id":"LaEr"},{"_id":"GradSch"}],"date_created":"2023-09-17T22:01:09Z","article_processing_charge":"Yes","publication_status":"published","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"last_name":"Kolupaiev","first_name":"Oleksii","full_name":"Kolupaiev, Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"scopus_import":"1","_id":"14343","ddc":["510"],"acknowledgement":"G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.","volume":11,"abstract":[{"text":"The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.","lang":"eng"}],"day":"23","doi":"10.1017/fms.2023.70","arxiv":1,"external_id":{"isi":["001051980200001"],"arxiv":["2301.05181"]},"isi":1,"year":"2023","citation":{"ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge University Press, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e74, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74."},"date_updated":"2023-12-13T12:24:23Z","language":[{"iso":"eng"}],"article_number":"e74","month":"08","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Forum of Mathematics, Sigma","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_size":852652,"checksum":"eb747420e6a88a7796fa934151957676","date_created":"2023-09-20T11:09:35Z","file_name":"2023_ForumMathematics_Cipolloni.pdf","content_type":"application/pdf","date_updated":"2023-09-20T11:09:35Z","success":1,"relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"14352"}],"oa":1,"publication_identifier":{"eissn":["2050-5094"]},"type":"journal_article","date_published":"2023-08-23T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}},{"acknowledgement":"J H gratefully acknowledges partial financial support by the ERC Advanced Grant 'RMTBeyond' No. 101020331.","volume":56,"ddc":["510"],"day":"11","doi":"10.1088/1751-8121/acfe62","arxiv":1,"abstract":[{"lang":"eng","text":"Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process $(Q_t)_{t\\in\\mathbb{R}}$ in the configuration space of a variable number of particles that is $|\\psi_t|^2$-distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission)."}],"citation":{"mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 56, no. 44, 445201, IOP Publishing, 2023, doi:<a href=\"https://doi.org/10.1088/1751-8121/acfe62\">10.1088/1751-8121/acfe62</a>.","short":"S.J. Henheik, R. Tumulka, Journal of Physics A: Mathematical and Theoretical 56 (2023).","ista":"Henheik SJ, Tumulka R. 2023. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 56(44), 445201.","ama":"Henheik SJ, Tumulka R. Creation rate of Dirac particles at a point source. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2023;56(44). doi:<a href=\"https://doi.org/10.1088/1751-8121/acfe62\">10.1088/1751-8121/acfe62</a>","apa":"Henheik, S. J., &#38; Tumulka, R. (2023). Creation rate of Dirac particles at a point source. <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1751-8121/acfe62\">https://doi.org/10.1088/1751-8121/acfe62</a>","ieee":"S. J. Henheik and R. Tumulka, “Creation rate of Dirac particles at a point source,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 56, no. 44. IOP Publishing, 2023.","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing, 2023. <a href=\"https://doi.org/10.1088/1751-8121/acfe62\">https://doi.org/10.1088/1751-8121/acfe62</a>."},"year":"2023","date_updated":"2023-12-13T13:01:25Z","external_id":{"isi":["001080908000001"],"arxiv":["2211.16606"]},"isi":1,"publisher":"IOP Publishing","article_type":"original","quality_controlled":"1","ec_funded":1,"file_date_updated":"2023-10-16T07:07:24Z","date_created":"2023-10-12T12:42:53Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","publication_status":"published","intvolume":"        56","title":"Creation rate of Dirac particles at a point source","scopus_import":"1","_id":"14421","issue":"44","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"full_name":"Tumulka, Roderich","first_name":"Roderich","last_name":"Tumulka"}],"file":[{"date_created":"2023-10-16T07:07:24Z","checksum":"5b68de147dd4c608b71a6e0e844d2ce9","file_size":721399,"date_updated":"2023-10-16T07:07:24Z","file_name":"2023_JourPhysics_Henheik.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","success":1,"file_id":"14429","creator":"dernst"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1751-8113"],"eissn":["1751-8121"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2023-10-11T00:00:00Z","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"oa_version":"Published Version","article_number":"445201","month":"10","has_accepted_license":"1","publication":"Journal of Physics A: Mathematical and Theoretical"},{"oa":1,"publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"date_published":"2023-10-31T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://doi.org/10.1142/S0129055X2360005X","open_access":"1"}],"month":"10","article_number":"2360005 ","oa_version":"Published Version","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"},{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"publication":"Reviews in Mathematical Physics","has_accepted_license":"1","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."}],"doi":"10.1142/s0129055x2360005x","arxiv":1,"day":"31","external_id":{"arxiv":["2301.05621"]},"date_updated":"2023-11-20T10:04:38Z","year":"2023","citation":{"ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023.","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>.","ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. 2023. doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>","apa":"Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2023). Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>","ista":"Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>, 2360005, World Scientific Publishing, 2023, doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>."},"acknowledgement":"We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427.","title":"Universality in low-dimensional BCS theory","publication_status":"epub_ahead","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"article_processing_charge":"Yes (in subscription journal)","date_created":"2023-11-15T23:48:14Z","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"},{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara","orcid":"0000-0002-9071-5880","last_name":"Roos","first_name":"Barbara"}],"_id":"14542","scopus_import":"1","article_type":"original","publisher":"World Scientific Publishing","quality_controlled":"1","ec_funded":1},{"page":"2083-2105","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Institute of Mathematical Statistics","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang","last_name":"Ji","first_name":"Hong Chang"}],"issue":"4","_id":"14667","scopus_import":"1","title":"Functional CLT for non-Hermitian random matrices","intvolume":"        59","publication_status":"published","article_processing_charge":"No","department":[{"_id":"LaEr"}],"date_created":"2023-12-10T23:01:00Z","volume":59,"acknowledgement":"The first author was partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated editor for carefully reading this paper and providing helpful comments that improved the quality of the article. Also the authors would like to thank Peter Forrester for pointing out the reference [12] that was absent in the previous version of the manuscript.","external_id":{"arxiv":["2112.11382"]},"date_updated":"2023-12-11T12:36:56Z","year":"2023","citation":{"chicago":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-AIHP1304\">https://doi.org/10.1214/22-AIHP1304</a>.","ieee":"L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.","apa":"Erdös, L., &#38; Ji, H. C. (2023). Functional CLT for non-Hermitian random matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AIHP1304\">https://doi.org/10.1214/22-AIHP1304</a>","ama":"Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2023;59(4):2083-2105. doi:<a href=\"https://doi.org/10.1214/22-AIHP1304\">10.1214/22-AIHP1304</a>","ista":"Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.","mla":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:<a href=\"https://doi.org/10.1214/22-AIHP1304\">10.1214/22-AIHP1304</a>.","short":"L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105."},"abstract":[{"lang":"eng","text":"For large dimensional non-Hermitian random matrices X with real or complex independent, identically distributed, centered entries, we consider the fluctuations of f (X) as a matrix where f is an analytic function around the spectrum of X. We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of A. We find a new formula for the variance of the traceless part that involves the Frobenius norm of A and the L2-norm of f on the boundary of the limiting spectrum. "},{"text":"On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction analytique sur un domaine qui contient le spectre de X. On prouve que, pour une matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie pour la variance de la composante de trace nulle, qui fait intervenir la norme de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.","lang":"fre"}],"doi":"10.1214/22-AIHP1304","arxiv":1,"day":"01","language":[{"iso":"eng"}],"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","month":"11","oa_version":"Preprint","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2112.11382","open_access":"1"}],"date_published":"2023-11-01T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"issn":["0246-0203"]}},{"publisher":"Institute of Mathematical Statistics","article_type":"original","ec_funded":1,"quality_controlled":"1","page":"2981-3009","department":[{"_id":"LaEr"}],"date_created":"2024-01-08T13:03:18Z","article_processing_charge":"No","publication_status":"published","intvolume":"        33","title":"Local laws for multiplication of random matrices","scopus_import":"1","_id":"14750","issue":"4","author":[{"full_name":"Ding, Xiucai","last_name":"Ding","first_name":"Xiucai"},{"last_name":"Ji","first_name":"Hong Chang","full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"acknowledgement":"The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments.","volume":33,"day":"01","doi":"10.1214/22-aap1882","arxiv":1,"abstract":[{"text":"Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \u0002 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \u0002μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. ","lang":"eng"}],"citation":{"ista":"Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009.","mla":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>.","short":"X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>.","ieee":"X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023.","ama":"Ding X, Ji HC. Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. 2023;33(4):2981-3009. doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>","apa":"Ding, X., &#38; Ji, H. C. (2023). Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>"},"year":"2023","date_updated":"2024-01-09T08:16:41Z","external_id":{"arxiv":["2010.16083"]},"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"oa_version":"Preprint","month":"08","publication":"The Annals of Applied Probability","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2010.16083","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_identifier":{"issn":["1050-5164"]},"oa":1,"type":"journal_article","date_published":"2023-08-01T00:00:00Z"},{"oa":1,"publication_identifier":{"issn":["1050-5164"]},"type":"journal_article","date_published":"2023-02-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.02728","open_access":"1"}],"month":"02","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"oa_version":"Preprint","publication":"The Annals of Applied Probability","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"language":[{"iso":"eng"}],"abstract":[{"text":"We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble.","lang":"eng"}],"day":"01","doi":"10.1214/22-aap1826","arxiv":1,"external_id":{"isi":["000946432400021"],"arxiv":["2108.02728"]},"isi":1,"citation":{"short":"K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>.","ista":"Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725.","apa":"Schnelli, K., &#38; Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. 2023;33(1):677-725. doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>."},"year":"2023","date_updated":"2024-01-10T13:31:46Z","volume":33,"acknowledgement":"K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","intvolume":"        33","title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","article_processing_charge":"No","date_created":"2024-01-10T09:23:31Z","department":[{"_id":"LaEr"}],"publication_status":"published","issue":"1","author":[{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"},{"orcid":"0000-0003-1559-1205","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"scopus_import":"1","_id":"14775","article_type":"original","publisher":"Institute of Mathematical Statistics","ec_funded":1,"quality_controlled":"1","page":"677-725"},{"publication":"Stochastic Processes and their Applications","has_accepted_license":"1","oa_version":"Published Version","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"month":"09","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2023-09-01T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["1879-209X"],"issn":["0304-4149"]},"oa":1,"file":[{"date_created":"2024-01-16T08:47:31Z","file_size":1870349,"checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","date_updated":"2024-01-16T08:47:31Z","content_type":"application/pdf","file_name":"2023_StochasticProcAppl_Ding.pdf","access_level":"open_access","success":1,"relation":"main_file","file_id":"14806","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","_id":"14780","author":[{"full_name":"Ding, Xiucai","last_name":"Ding","first_name":"Xiucai"},{"first_name":"Hong Chang","last_name":"Ji","full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"publication_status":"published","date_created":"2024-01-10T09:29:25Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (in subscription journal)","title":"Spiked multiplicative random matrices and principal components","intvolume":"       163","page":"25-60","ec_funded":1,"quality_controlled":"1","file_date_updated":"2024-01-16T08:47:31Z","publisher":"Elsevier","article_type":"original","date_updated":"2024-01-16T08:49:51Z","year":"2023","citation":{"ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and their Applications</i>. 2023;163:25-60. doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>","apa":"Ding, X., &#38; Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>.","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” <i>Stochastic Processes and their Applications</i>, vol. 163. Elsevier, pp. 25–60, 2023.","mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>, vol. 163, Elsevier, 2023, pp. 25–60, doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>.","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60."},"isi":1,"external_id":{"isi":["001113615900001"],"arxiv":["2302.13502"]},"arxiv":1,"doi":"10.1016/j.spa.2023.05.009","day":"01","abstract":[{"text":"In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix.","lang":"eng"}],"acknowledgement":"The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","volume":163,"ddc":["510"]},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"oa_version":"Preprint","month":"11","publication":"The Annals of Probability","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0091-1798"]},"oa":1,"type":"journal_article","date_published":"2023-11-01T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2206.04448","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2024-01-22T08:08:41Z","department":[{"_id":"LaEr"}],"publication_status":"published","intvolume":"        51","title":"On the rightmost eigenvalue of non-Hermitian random matrices","_id":"14849","issue":"6","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu"}],"publisher":"Institute of Mathematical Statistics","article_type":"original","quality_controlled":"1","ec_funded":1,"page":"2192-2242","day":"01","arxiv":1,"doi":"10.1214/23-aop1643","abstract":[{"text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.","lang":"eng"}],"citation":{"ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2023;51(6):2192-2242. doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>."},"year":"2023","date_updated":"2024-01-23T10:56:30Z","external_id":{"arxiv":["2206.04448"]},"acknowledgement":"The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation.","volume":51},{"citation":{"ista":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 190(7), 128.","short":"S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics 190 (2023).","mla":"Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” <i>Journal of Statistical Physics</i>, vol. 190, no. 7, 128, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s10955-023-03132-4\">10.1007/s10955-023-03132-4</a>.","ieee":"S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation hypothesis for translation invariant spin systems,” <i>Journal of Statistical Physics</i>, vol. 190, no. 7. Springer Nature, 2023.","chicago":"Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” <i>Journal of Statistical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s10955-023-03132-4\">https://doi.org/10.1007/s10955-023-03132-4</a>.","ama":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis for translation invariant spin systems. <i>Journal of Statistical Physics</i>. 2023;190(7). doi:<a href=\"https://doi.org/10.1007/s10955-023-03132-4\">10.1007/s10955-023-03132-4</a>","apa":"Sugimoto, S., Henheik, S. J., Riabov, V., &#38; Erdös, L. (2023). Eigenstate thermalisation hypothesis for translation invariant spin systems. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-023-03132-4\">https://doi.org/10.1007/s10955-023-03132-4</a>"},"year":"2023","date_updated":"2023-12-13T11:38:44Z","external_id":{"isi":["001035677200002"],"arxiv":["2304.04213"]},"isi":1,"day":"21","doi":"10.1007/s10955-023-03132-4","arxiv":1,"abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with L-body interactions, where L is the number of spins. This mathematically verifies the observation first made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130) that the ETH may hold for systems with additional translational symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interaction."}],"acknowledgement":"LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond” No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study (WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The University of Tokyo.","volume":190,"ddc":["510","530"],"scopus_import":"1","_id":"13317","issue":"7","author":[{"full_name":"Sugimoto, Shoki","first_name":"Shoki","last_name":"Sugimoto"},{"last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","last_name":"Riabov","first_name":"Volodymyr"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"}],"date_created":"2023-07-30T22:01:02Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (in subscription journal)","publication_status":"published","intvolume":"       190","title":"Eigenstate thermalisation hypothesis for translation invariant spin systems","quality_controlled":"1","ec_funded":1,"file_date_updated":"2023-07-31T07:49:31Z","publisher":"Springer Nature","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2023-07-21T00:00:00Z","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"oa":1,"file":[{"checksum":"c2ef6b2aecfee1ad6d03fab620507c2c","file_size":612755,"date_created":"2023-07-31T07:49:31Z","content_type":"application/pdf","file_name":"2023_JourStatPhysics_Sugimoto.pdf","date_updated":"2023-07-31T07:49:31Z","relation":"main_file","success":1,"access_level":"open_access","creator":"dernst","file_id":"13325"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","has_accepted_license":"1","publication":"Journal of Statistical Physics","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"oa_version":"Published Version","article_number":"128","month":"07","language":[{"iso":"eng"}]},{"external_id":{"isi":["000950650200005"],"arxiv":["2108.13694"]},"isi":1,"year":"2023","citation":{"chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>.","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>","apa":"Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>.","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13."},"date_updated":"2023-10-17T12:48:10Z","abstract":[{"lang":"eng","text":"We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices."}],"day":"08","doi":"10.1214/23-ECP516","arxiv":1,"ddc":["510"],"volume":28,"acknowledgement":"G. Dubach gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","first_name":"Guillaume"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"12683","intvolume":"        28","title":"Dynamics of a rank-one perturbation of a Hermitian matrix","date_created":"2023-02-26T23:01:01Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"publication_status":"published","file_date_updated":"2023-02-27T09:43:27Z","quality_controlled":"1","ec_funded":1,"page":"1-13","article_type":"original","publisher":"Institute of Mathematical Statistics","type":"journal_article","date_published":"2023-02-08T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["1083-589X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"date_updated":"2023-02-27T09:43:27Z","content_type":"application/pdf","file_name":"2023_ElectCommProbability_Dubach.pdf","date_created":"2023-02-27T09:43:27Z","file_size":479105,"checksum":"a1c6f0a3e33688fd71309c86a9aad86e","file_id":"12692","creator":"dernst","relation":"main_file","success":1,"access_level":"open_access"}],"has_accepted_license":"1","publication":"Electronic Communications in Probability","month":"02","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"oa_version":"Published Version","language":[{"iso":"eng"}]},{"page":"1063-1079","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Bernoulli Society for Mathematical Statistics and Probability","author":[{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","last_name":"Xu","orcid":"0000-0003-1559-1205","full_name":"Xu, Yuanyuan"}],"issue":"2","_id":"12707","scopus_import":"1","title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","intvolume":"        29","publication_status":"published","article_processing_charge":"No","department":[{"_id":"LaEr"}],"date_created":"2023-03-05T23:01:05Z","volume":29,"isi":1,"external_id":{"arxiv":["2112.12093 "],"isi":["000947270100008"]},"date_updated":"2023-10-04T10:21:07Z","year":"2023","citation":{"mla":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>, vol. 29, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>.","short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.","ama":"Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner matrices. <i>Bernoulli</i>. 2023;29(2):1063-1079. doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>","apa":"Erdös, L., &#38; Xu, Y. (2023). Small deviation estimates for the largest eigenvalue of Wigner matrices. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>","ieee":"L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue of Wigner matrices,” <i>Bernoulli</i>, vol. 29, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1063–1079, 2023.","chicago":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2023. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>."},"abstract":[{"lang":"eng","text":"We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail."}],"arxiv":1,"doi":"10.3150/22-BEJ1490","day":"01","language":[{"iso":"eng"}],"publication":"Bernoulli","month":"05","oa_version":"Preprint","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"date_published":"2023-05-01T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"issn":["1350-7265"]}},{"publication":"Annals of Applied Probability","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"oa_version":"Preprint","month":"02","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2023-02-01T00:00:00Z","publication_identifier":{"issn":["1050-5164"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2012.13218","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","scopus_import":"1","_id":"12761","issue":"1","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","department":[{"_id":"LaEr"}],"date_created":"2023-03-26T22:01:08Z","publication_status":"published","intvolume":"        33","title":"Functional central limit theorems for Wigner matrices","quality_controlled":"1","ec_funded":1,"page":"447-489","publisher":"Institute of Mathematical Statistics","article_type":"original","year":"2023","citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. 2023;33(1):447-489. doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central Limit Theorems for Wigner Matrices.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems for Wigner matrices,” <i>Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 447–489, 2023.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489.","mla":"Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.” <i>Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 447–89, doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489."},"date_updated":"2023-10-17T12:48:52Z","external_id":{"arxiv":["2012.13218"],"isi":["000946432400015"]},"isi":1,"day":"01","arxiv":1,"doi":"10.1214/22-AAP1820","abstract":[{"text":"We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent\r\nmultiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"volume":33,"acknowledgement":"The second author is partially funded by the ERC Advanced Grant “RMTBEYOND” No. 101020331. The third author is supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation."},{"language":[{"iso":"eng"}],"month":"07","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"publication":"Communications in Mathematical Physics","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"date_created":"2023-10-04T12:09:18Z","checksum":"72057940f76654050ca84a221f21786c","file_size":859967,"date_updated":"2023-10-04T12:09:18Z","file_name":"2023_CommMathPhysics_Cipolloni.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","success":1,"file_id":"14397","creator":"dernst"}],"oa":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_published":"2023-07-01T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","publisher":"Springer Nature","file_date_updated":"2023-10-04T12:09:18Z","page":"1665-1700","quality_controlled":"1","ec_funded":1,"title":"On the spectral form factor for random matrices","intvolume":"       401","publication_status":"published","date_created":"2023-04-02T22:01:11Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"_id":"12792","scopus_import":"1","ddc":["510"],"volume":401,"acknowledgement":"We are grateful to the authors of [25] for sharing with us their insights and preliminary numerical results. We are especially thankful to Stephen Shenker for very valuable advice over several email communications. Helpful comments on the manuscript from Peter Forrester and from the anonymous referees are also acknowledged.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\" No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","abstract":[{"lang":"eng","text":"In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics."}],"doi":"10.1007/s00220-023-04692-y","day":"01","isi":1,"external_id":{"isi":["000957343500001"]},"date_updated":"2023-10-04T12:10:31Z","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","mla":"Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” <i>Communications in Mathematical Physics</i>, vol. 401. Springer Nature, pp. 1665–1700, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. 2023;401:1665-1700. doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>"},"year":"2023"},{"publication_status":"published","department":[{"_id":"LaEr"}],"date_created":"2022-04-24T22:01:44Z","article_processing_charge":"No","title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","intvolume":"       393","_id":"11332","scopus_import":"1","author":[{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli","first_name":"Kevin"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","last_name":"Xu","first_name":"Yuanyuan","full_name":"Xu, Yuanyuan"}],"publisher":"Springer Nature","article_type":"original","page":"839-907","quality_controlled":"1","ec_funded":1,"file_date_updated":"2022-08-05T06:01:13Z","arxiv":1,"doi":"10.1007/s00220-022-04377-y","day":"01","abstract":[{"text":"We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles.","lang":"eng"}],"date_updated":"2023-08-03T06:34:24Z","citation":{"mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 393, Springer Nature, 2022, pp. 839–907, doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>.","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","ista":"Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. 2022;393:839-907. doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>","apa":"Schnelli, K., &#38; Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 393. Springer Nature, pp. 839–907, 2022.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>."},"year":"2022","isi":1,"external_id":{"arxiv":["2102.04330"],"isi":["000782737200001"]},"acknowledgement":"Kevin Schnelli is supported in parts by the Swedish Research Council Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","volume":393,"ddc":["510"],"oa_version":"Published Version","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"month":"07","publication":"Communications in Mathematical Physics","has_accepted_license":"1","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2022-07-01T00:00:00Z","type":"journal_article","file":[{"creator":"dernst","file_id":"11726","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_name":"2022_CommunMathPhys_Schnelli.pdf","date_updated":"2022-08-05T06:01:13Z","file_size":1141462,"checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","date_created":"2022-08-05T06:01:13Z"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"language":[{"iso":"eng"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"publication":"Journal of Statistical Physics","has_accepted_license":"1","month":"07","article_number":"5","oa_version":"Published Version","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"file_id":"11746","creator":"dernst","relation":"main_file","access_level":"open_access","success":1,"date_updated":"2022-08-08T07:36:34Z","content_type":"application/pdf","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","date_created":"2022-08-08T07:36:34Z","checksum":"b398c4dbf65f71d417981d6e366427e9","file_size":419563}],"date_published":"2022-07-29T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"file_date_updated":"2022-08-08T07:36:34Z","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Springer Nature","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha"},{"last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"_id":"11732","scopus_import":"1","title":"The BCS energy gap at high density","intvolume":"       189","publication_status":"published","article_processing_charge":"Yes (via OA deal)","date_created":"2022-08-05T11:36:56Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"ddc":["530"],"acknowledgement":"We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)","volume":189,"isi":1,"external_id":{"isi":["000833007200002"]},"date_updated":"2023-09-05T14:57:49Z","citation":{"ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>, vol. 189, 5, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>.","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” <i>Journal of Statistical Physics</i>, vol. 189. Springer Nature, 2022.","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>.","apa":"Henheik, S. J., &#38; Lauritsen, A. B. (2022). The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>","ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. 2022;189. doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>"},"year":"2022","abstract":[{"lang":"eng","text":"We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature."}],"doi":"10.1007/s10955-022-02965-9","day":"29"},{"acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","volume":63,"isi":1,"external_id":{"arxiv":["2012.15238"],"isi":["000739446000009"]},"date_updated":"2023-08-02T13:44:32Z","year":"2022","citation":{"apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0051632\">https://doi.org/10.1063/5.0051632</a>","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. 2022;63(1). doi:<a href=\"https://doi.org/10.1063/5.0051632\">10.1063/5.0051632</a>","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0051632\">https://doi.org/10.1063/5.0051632</a>.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 1. AIP Publishing, 2022.","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0051632\">10.1063/5.0051632</a>.","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901."},"abstract":[{"text":"We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.","lang":"eng"}],"doi":"10.1063/5.0051632","arxiv":1,"day":"03","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"AIP Publishing","author":[{"last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"}],"issue":"1","_id":"10600","title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","intvolume":"        63","publication_status":"published","date_created":"2022-01-03T12:19:48Z","article_processing_charge":"No","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2012.15238"}],"date_published":"2022-01-03T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"language":[{"iso":"eng"}],"keyword":["mathematical physics","statistical and nonlinear physics"],"publication":"Journal of Mathematical Physics","month":"01","article_number":"011901","oa_version":"Preprint","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}]},{"publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2022-01-11T00:00:00Z","file":[{"date_created":"2022-01-14T07:27:45Z","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","file_size":505804,"date_updated":"2022-01-14T07:27:45Z","content_type":"application/pdf","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"10624","creator":"cchlebak"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"oa_version":"Published Version","article_number":"3","month":"01","has_accepted_license":"1","publication":"Mathematical Physics, Analysis and Geometry","keyword":["geometry and topology","mathematical physics"],"language":[{"iso":"eng"}],"day":"11","doi":"10.1007/s11040-021-09415-0","arxiv":1,"abstract":[{"lang":"eng","text":"We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory."}],"year":"2022","citation":{"short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","mla":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 25, no. 1, 3, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s11040-021-09415-0\">10.1007/s11040-021-09415-0</a>.","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11040-021-09415-0\">https://doi.org/10.1007/s11040-021-09415-0</a>","ama":"Henheik SJ. The BCS critical temperature at high density. <i>Mathematical Physics, Analysis and Geometry</i>. 2022;25(1). doi:<a href=\"https://doi.org/10.1007/s11040-021-09415-0\">10.1007/s11040-021-09415-0</a>","chicago":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s11040-021-09415-0\">https://doi.org/10.1007/s11040-021-09415-0</a>.","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 25, no. 1. Springer Nature, 2022."},"date_updated":"2023-08-02T13:51:52Z","external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"isi":1,"acknowledgement":"I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions.","volume":25,"ddc":["514"],"article_processing_charge":"Yes (via OA deal)","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_created":"2022-01-13T15:40:53Z","publication_status":"published","intvolume":"        25","title":"The BCS critical temperature at high density","scopus_import":"1","_id":"10623","issue":"1","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik"}],"publisher":"Springer Nature","article_type":"original","quality_controlled":"1","ec_funded":1,"file_date_updated":"2022-01-14T07:27:45Z"},{"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"success":1,"relation":"main_file","access_level":"open_access","file_id":"10647","creator":"cchlebak","date_created":"2022-01-19T09:41:14Z","file_size":357547,"checksum":"7e8e69b76e892c305071a4736131fe18","date_updated":"2022-01-19T09:41:14Z","file_name":"2022_LettersMathPhys_Henheik.pdf","content_type":"application/pdf"}],"oa":1,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"date_published":"2022-01-18T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"keyword":["mathematical physics","statistical and nonlinear physics"],"month":"01","article_number":"9","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"publication":"Letters in Mathematical Physics","has_accepted_license":"1","ddc":["530"],"acknowledgement":"J. H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for very helpful comments and discussions and Jürg Fröhlich for references to the literature. Open Access funding enabled and organized by Projekt DEAL.","volume":112,"abstract":[{"text":"Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences.","lang":"eng"}],"doi":"10.1007/s11005-021-01494-y","arxiv":1,"day":"18","isi":1,"external_id":{"arxiv":["2106.13780"],"isi":["000744930400001"]},"date_updated":"2023-08-02T13:57:02Z","year":"2022","citation":{"mla":"Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>, vol. 112, no. 1, 9, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s11005-021-01494-y\">10.1007/s11005-021-01494-y</a>.","short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","ista":"Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9.","apa":"Henheik, S. J., Teufel, S., &#38; Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-021-01494-y\">https://doi.org/10.1007/s11005-021-01494-y</a>","ama":"Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical Physics</i>. 2022;112(1). doi:<a href=\"https://doi.org/10.1007/s11005-021-01494-y\">10.1007/s11005-021-01494-y</a>","ieee":"S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” <i>Letters in Mathematical Physics</i>, vol. 112, no. 1. Springer Nature, 2022.","chicago":"Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s11005-021-01494-y\">https://doi.org/10.1007/s11005-021-01494-y</a>."},"article_type":"original","publisher":"Springer Nature","file_date_updated":"2022-01-19T09:41:14Z","ec_funded":1,"quality_controlled":"1","title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","intvolume":"       112","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"article_processing_charge":"No","date_created":"2022-01-18T16:18:25Z","author":[{"orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"},{"first_name":"Tom","last_name":"Wessel","full_name":"Wessel, Tom"}],"issue":"1","_id":"10642"},{"author":[{"orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"}],"_id":"10643","intvolume":"        10","title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_created":"2022-01-18T16:18:51Z","article_processing_charge":"Yes","publication_status":"published","file_date_updated":"2022-01-19T09:27:43Z","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Cambridge University Press","external_id":{"isi":["000743615000001"],"arxiv":["2012.15239"]},"isi":1,"year":"2022","citation":{"ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e4, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4."},"date_updated":"2023-08-02T13:53:11Z","abstract":[{"lang":"eng","text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"}],"day":"18","doi":"10.1017/fms.2021.80","arxiv":1,"ddc":["510"],"volume":10,"acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","has_accepted_license":"1","publication":"Forum of Mathematics, Sigma","article_number":"e4","month":"01","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"oa_version":"Published Version","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"language":[{"iso":"eng"}],"type":"journal_article","date_published":"2022-01-18T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["2050-5094"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"file_name":"2022_ForumMathSigma_Henheik.pdf","content_type":"application/pdf","date_updated":"2022-01-19T09:27:43Z","checksum":"87592a755adcef22ea590a99dc728dd3","file_size":705323,"date_created":"2022-01-19T09:27:43Z","creator":"cchlebak","file_id":"10646","success":1,"relation":"main_file","access_level":"open_access"}]}]