[{"status":"public","abstract":[{"lang":"eng","text":"Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. "}],"ec_funded":1,"keyword":["General Mathematics"],"intvolume":" 106","citation":{"short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","ama":"Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 2022;106(4):3865-3894. doi:10.1112/jlms.12676","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12676.","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12676","ista":"Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4), 3865–3894.","mla":"Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:10.1112/jlms.12676.","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” Journal of the London Mathematical Society, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022."},"day":"18","publication_status":"published","oa":1,"title":"The isometry group of Wasserstein spaces: The Hilbertian case","article_type":"original","month":"09","_id":"12214","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"LaEr"}],"acknowledgement":"Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). ","isi":1,"volume":106,"year":"2022","date_created":"2023-01-16T09:46:13Z","quality_controlled":"1","page":"3865-3894","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020"}],"date_updated":"2023-08-04T09:24:17Z","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2102.02037","open_access":"1"}],"scopus_import":"1","article_processing_charge":"No","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","doi":"10.1112/jlms.12676","publisher":"Wiley","issue":"4","publication":"Journal of the London Mathematical Society","author":[{"first_name":"György Pál","full_name":"Gehér, György Pál","last_name":"Gehér"},{"last_name":"Titkos","first_name":"Tamás","full_name":"Titkos, Tamás"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","last_name":"Virosztek","full_name":"Virosztek, Daniel","first_name":"Daniel"}],"external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"oa_version":"Preprint","date_published":"2022-09-18T00:00:00Z"},{"article_processing_charge":"No","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"date_updated":"2023-08-04T09:33:52Z","page":"3981-4002","quality_controlled":"1","date_created":"2023-01-16T09:50:26Z","year":"2022","volume":23,"isi":1,"file":[{"relation":"main_file","checksum":"5582f059feeb2f63e2eb68197a34d7dc","file_size":1333638,"creator":"dernst","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","date_created":"2023-01-27T11:06:47Z","file_id":"12424","content_type":"application/pdf","date_updated":"2023-01-27T11:06:47Z","access_level":"open_access","success":1}],"date_published":"2022-11-01T00:00:00Z","oa_version":"Published Version","external_id":{"isi":["000796323500001"]},"ddc":["510"],"author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio"},{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"publication":"Annales Henri Poincaré","issue":"11","publisher":"Springer Nature","doi":"10.1007/s00023-022-01188-8","file_date_updated":"2023-01-27T11:06:47Z","type":"journal_article","language":[{"iso":"eng"}],"has_accepted_license":"1","day":"01","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 2022;23(11):3981-4002. doi:10.1007/s00023-022-01188-8","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré. Springer Nature, 2022. https://doi.org/10.1007/s00023-022-01188-8.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-022-01188-8","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:10.1007/s00023-022-01188-8."},"intvolume":" 23","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"abstract":[{"lang":"eng","text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold."}],"status":"public","department":[{"_id":"LaEr"}],"acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12232","month":"11","article_type":"original","oa":1,"title":"Density of small singular values of the shifted real Ginibre ensemble","publication_status":"published"},{"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 2022;63(10). doi:10.1063/5.0104290","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104290","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104290.","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:10.1063/5.0104290.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no. 10. AIP Publishing, 2022."},"intvolume":" 63","day":"14","has_accepted_license":"1","article_number":"103303","status":"public","abstract":[{"text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. ","lang":"eng"}],"ec_funded":1,"acknowledgement":"The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","department":[{"_id":"LaEr"}],"oa":1,"title":"Directional extremal statistics for Ginibre eigenvalues","publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12243","month":"10","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":63,"isi":1,"file":[{"file_size":7356807,"creator":"dernst","relation":"main_file","checksum":"2db278ae5b07f345a7e3fec1f92b5c33","content_type":"application/pdf","file_id":"12436","date_created":"2023-01-30T08:01:10Z","date_updated":"2023-01-30T08:01:10Z","access_level":"open_access","success":1,"file_name":"2022_JourMathPhysics_Cipolloni2.pdf"}],"quality_controlled":"1","date_created":"2023-01-16T09:52:58Z","year":"2022","date_updated":"2023-08-04T09:40:02Z","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"issue":"10","publication":"Journal of Mathematical Physics","ddc":["510","530"],"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","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"oa_version":"Published Version","external_id":{"arxiv":["2206.04443"],"isi":["000869715800001"]},"date_published":"2022-10-14T00:00:00Z","arxiv":1,"language":[{"iso":"eng"}],"file_date_updated":"2023-01-30T08:01:10Z","type":"journal_article","doi":"10.1063/5.0104290","publisher":"AIP Publishing"},{"has_accepted_license":"1","day":"12","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” Electronic Journal of Probability, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:10.1214/22-ejp838.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/22-ejp838.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-ejp838","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38."},"intvolume":" 27","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"ec_funded":1,"abstract":[{"text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale.","lang":"eng"}],"status":"public","department":[{"_id":"LaEr"}],"acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","month":"09","_id":"12290","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","publication_status":"published","oa":1,"title":"Optimal multi-resolvent local laws for Wigner matrices","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","scopus_import":"1","publication_identifier":{"eissn":["1083-6489"]},"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"date_updated":"2023-08-04T10:32:23Z","year":"2022","date_created":"2023-01-16T10:04:38Z","quality_controlled":"1","page":"1-38","isi":1,"file":[{"date_created":"2023-01-30T11:59:21Z","content_type":"application/pdf","file_id":"12464","access_level":"open_access","success":1,"date_updated":"2023-01-30T11:59:21Z","file_name":"2022_ElecJournProbability_Cipolloni.pdf","file_size":502149,"creator":"dernst","relation":"main_file","checksum":"bb647b48fbdb59361210e425c220cdcb"}],"volume":27,"date_published":"2022-09-12T00:00:00Z","oa_version":"Published Version","external_id":{"isi":["000910863700003"]},"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"ddc":["510"],"publication":"Electronic Journal of Probability","publisher":"Institute of Mathematical Statistics","doi":"10.1214/22-ejp838","type":"journal_article","file_date_updated":"2023-01-30T11:59:21Z","language":[{"iso":"eng"}]},{"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2012.15238"}],"publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"date_updated":"2023-08-02T13:44:32Z","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"quality_controlled":"1","date_created":"2022-01-03T12:19:48Z","year":"2022","volume":63,"isi":1,"date_published":"2022-01-03T00:00:00Z","oa_version":"Preprint","external_id":{"arxiv":["2012.15238"],"isi":["000739446000009"]},"author":[{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"issue":"1","publication":"Journal of Mathematical Physics","publisher":"AIP Publishing","doi":"10.1063/5.0051632","type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"day":"03","citation":{"short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 2022;63(1). doi:10.1063/5.0051632","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0051632.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0051632","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” Journal of Mathematical Physics, 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.” Journal of Mathematical Physics, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632."},"intvolume":" 63","keyword":["mathematical physics","statistical and nonlinear physics"],"ec_funded":1,"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"}],"article_number":"011901","status":"public","acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10600","month":"01","article_type":"original","oa":1,"title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","publication_status":"published"},{"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"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.","oa":1,"title":"The BCS critical temperature at high density","publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10623","month":"01","keyword":["geometry and topology","mathematical physics"],"citation":{"short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","ama":"Henheik SJ. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0","chicago":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0.","apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","mla":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022, doi:10.1007/s11040-021-09415-0.","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022."},"intvolume":" 25","day":"11","has_accepted_license":"1","article_number":"3","status":"public","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."}],"ec_funded":1,"issue":"1","publication":"Mathematical Physics, Analysis and Geometry","ddc":["514"],"author":[{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik"}],"external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"oa_version":"Published Version","date_published":"2022-01-11T00:00:00Z","language":[{"iso":"eng"}],"arxiv":1,"file_date_updated":"2022-01-14T07:27:45Z","type":"journal_article","doi":"10.1007/s11040-021-09415-0","publisher":"Springer Nature","publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","volume":25,"isi":1,"file":[{"checksum":"d44f8123a52592a75b2c3b8ee2cd2435","relation":"main_file","creator":"cchlebak","file_size":505804,"file_name":"2022_MathPhyAnalGeo_Henheik.pdf","date_updated":"2022-01-14T07:27:45Z","success":1,"access_level":"open_access","date_created":"2022-01-14T07:27:45Z","file_id":"10624","content_type":"application/pdf"}],"quality_controlled":"1","date_created":"2022-01-13T15:40:53Z","year":"2022","date_updated":"2023-08-02T13:51:52Z","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}]},{"date_published":"2022-01-18T00:00:00Z","oa_version":"Published Version","external_id":{"isi":["000744930400001"],"arxiv":["2106.13780"]},"ddc":["530"],"author":[{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"},{"first_name":"Tom","full_name":"Wessel, Tom","last_name":"Wessel"}],"issue":"1","publication":"Letters in Mathematical Physics","publisher":"Springer Nature","doi":"10.1007/s11005-021-01494-y","file_date_updated":"2022-01-19T09:41:14Z","type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"date_updated":"2023-08-02T13:57:02Z","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"quality_controlled":"1","date_created":"2022-01-18T16:18:25Z","year":"2022","volume":112,"isi":1,"file":[{"file_name":"2022_LettersMathPhys_Henheik.pdf","success":1,"access_level":"open_access","date_updated":"2022-01-19T09:41:14Z","file_id":"10647","content_type":"application/pdf","date_created":"2022-01-19T09:41:14Z","checksum":"7e8e69b76e892c305071a4736131fe18","relation":"main_file","creator":"cchlebak","file_size":357547}],"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.","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10642","month":"01","article_type":"original","oa":1,"title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","publication_status":"published","has_accepted_license":"1","day":"18","intvolume":" 112","citation":{"short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","ama":"Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 2022;112(1). doi:10.1007/s11005-021-01494-y","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.","chicago":"Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y.","apa":"Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y","ieee":"S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” Letters in Mathematical Physics, vol. 112, no. 1. Springer Nature, 2022.","mla":"Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics, vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y."},"keyword":["mathematical physics","statistical and nonlinear physics"],"ec_funded":1,"abstract":[{"lang":"eng","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."}],"article_number":"9","status":"public"},{"article_number":"e4","status":"public","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"}],"ec_funded":1,"keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"intvolume":" 10","citation":{"mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.80","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.","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80.","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022)."},"day":"18","has_accepted_license":"1","title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","oa":1,"publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"01","_id":"10643","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"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.","volume":10,"isi":1,"file":[{"creator":"cchlebak","file_size":705323,"checksum":"87592a755adcef22ea590a99dc728dd3","relation":"main_file","access_level":"open_access","date_updated":"2022-01-19T09:27:43Z","success":1,"file_id":"10646","date_created":"2022-01-19T09:27:43Z","content_type":"application/pdf","file_name":"2022_ForumMathSigma_Henheik.pdf"}],"quality_controlled":"1","date_created":"2022-01-18T16:18:51Z","year":"2022","date_updated":"2023-08-02T13:53:11Z","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"publication_identifier":{"eissn":["2050-5094"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes","arxiv":1,"language":[{"iso":"eng"}],"file_date_updated":"2022-01-19T09:27:43Z","type":"journal_article","doi":"10.1017/fms.2021.80","publisher":"Cambridge University Press","publication":"Forum of Mathematics, Sigma","ddc":["510"],"author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"last_name":"Teufel","full_name":"Teufel, Stefan","first_name":"Stefan"}],"external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]},"oa_version":"Published Version","date_published":"2022-01-18T00:00:00Z"},{"citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. Journal of Functional Analysis. 2022;282(8). doi:10.1016/j.jfa.2022.109394","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” Journal of Functional Analysis, vol. 282, no. 8. Elsevier, 2022.","mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis, vol. 282, no. 8, 109394, Elsevier, 2022, doi:10.1016/j.jfa.2022.109394.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Thermalisation for Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109394","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109394."},"intvolume":" 282","has_accepted_license":"1","day":"15","abstract":[{"lang":"eng","text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices."}],"article_number":"109394","status":"public","department":[{"_id":"LaEr"}],"acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","article_type":"original","oa":1,"title":"Thermalisation for Wigner matrices","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"04","_id":"10732","scopus_import":"1","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","volume":282,"file":[{"checksum":"b75fdad606ab507dc61109e0907d86c0","relation":"main_file","creator":"dernst","file_size":652573,"file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","access_level":"open_access","success":1,"date_updated":"2022-07-29T07:22:08Z","content_type":"application/pdf","date_created":"2022-07-29T07:22:08Z","file_id":"11690"}],"isi":1,"date_updated":"2023-08-02T14:12:35Z","quality_controlled":"1","date_created":"2022-02-06T23:01:30Z","year":"2022","ddc":["500"],"author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"issue":"8","publication":"Journal of Functional Analysis","date_published":"2022-04-15T00:00:00Z","oa_version":"Published Version","external_id":{"arxiv":["2102.09975"],"isi":["000781239100004"]},"file_date_updated":"2022-07-29T07:22:08Z","type":"journal_article","language":[{"iso":"eng"}],"arxiv":1,"publisher":"Elsevier","doi":"10.1016/j.jfa.2022.109394"},{"date_published":"2022-10-01T00:00:00Z","external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"oa_version":"Preprint","author":[{"full_name":"Reker, Jana","first_name":"Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9"}],"issue":"4","publication":"Random Matrices: Theory and Applications","publisher":"World Scientific","doi":"10.1142/s2010326322500368","type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.03906"}],"scopus_import":"1","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"date_updated":"2023-08-03T06:32:22Z","date_created":"2022-04-08T07:11:12Z","year":"2022","quality_controlled":"1","isi":1,"volume":11,"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"month":"10","_id":"11135","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","publication_status":"published","oa":1,"title":"On the operator norm of a Hermitian random matrix with correlated entries","day":"01","intvolume":" 11","citation":{"ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications. World Scientific, 2022. https://doi.org/10.1142/s2010326322500368.","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. World Scientific. https://doi.org/10.1142/s2010326322500368","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” Random Matrices: Theory and Applications, vol. 11, no. 4. World Scientific, 2022.","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications, vol. 11, no. 4, 2250036, World Scientific, 2022, doi:10.1142/s2010326322500368.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 2022;11(4). doi:10.1142/s2010326322500368"},"keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"abstract":[{"text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.","lang":"eng"}],"status":"public","article_number":"2250036"},{"citation":{"mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics, vol. 393, Springer Nature, 2022, pp. 839–907, doi:10.1007/s00220-022-04377-y.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” Communications in Mathematical Physics, vol. 393. Springer Nature, pp. 839–907, 2022.","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.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s00220-022-04377-y.","apa":"Schnelli, K., & Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-022-04377-y","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 2022;393:839-907. doi:10.1007/s00220-022-04377-y","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907."},"intvolume":" 393","day":"01","has_accepted_license":"1","status":"public","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"}],"ec_funded":1,"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.","department":[{"_id":"LaEr"}],"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","oa":1,"publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"11332","month":"07","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"scopus_import":"1","article_processing_charge":"No","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":393,"isi":1,"file":[{"file_name":"2022_CommunMathPhys_Schnelli.pdf","date_created":"2022-08-05T06:01:13Z","file_id":"11726","content_type":"application/pdf","date_updated":"2022-08-05T06:01:13Z","success":1,"access_level":"open_access","relation":"main_file","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_size":1141462,"creator":"dernst"}],"quality_controlled":"1","page":"839-907","date_created":"2022-04-24T22:01:44Z","year":"2022","date_updated":"2023-08-03T06:34:24Z","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication":"Communications in Mathematical Physics","ddc":["510"],"author":[{"full_name":"Schnelli, Kevin","first_name":"Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231"},{"last_name":"Xu","first_name":"Yuanyuan","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"external_id":{"isi":["000782737200001"],"arxiv":["2102.04330"]},"oa_version":"Published Version","date_published":"2022-07-01T00:00:00Z","arxiv":1,"language":[{"iso":"eng"}],"file_date_updated":"2022-08-05T06:01:13Z","type":"journal_article","doi":"10.1007/s00220-022-04377-y","publisher":"Springer Nature"},{"type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"publisher":"Institute of Mathematical Statistics","doi":"10.1214/21-AOP1552","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"issue":"3","publication":"Annals of Probability","date_published":"2022-05-01T00:00:00Z","external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"oa_version":"Preprint","volume":50,"isi":1,"date_updated":"2023-08-03T07:16:53Z","quality_controlled":"1","page":"984-1012","date_created":"2022-05-29T22:01:53Z","year":"2022","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"article_processing_charge":"No","article_type":"original","oa":1,"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"11418","month":"05","acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","department":[{"_id":"LaEr"}],"abstract":[{"lang":"eng","text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048)."}],"status":"public","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 2022;50(3):984-1012. doi:10.1214/21-AOP1552","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1552.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1552","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” Annals of Probability, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:10.1214/21-AOP1552."},"intvolume":" 50","day":"01"},{"article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"scopus_import":"1","quality_controlled":"1","year":"2022","date_created":"2022-08-05T11:36:56Z","date_updated":"2023-09-05T14:57:49Z","project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"volume":189,"file":[{"file_size":419563,"creator":"dernst","relation":"main_file","checksum":"b398c4dbf65f71d417981d6e366427e9","date_created":"2022-08-08T07:36:34Z","file_id":"11746","content_type":"application/pdf","success":1,"date_updated":"2022-08-08T07:36:34Z","access_level":"open_access","file_name":"2022_JourStatisticalPhysics_Henheik.pdf"}],"isi":1,"oa_version":"Published Version","external_id":{"isi":["000833007200002"]},"date_published":"2022-07-29T00:00:00Z","publication":"Journal of Statistical Physics","ddc":["530"],"author":[{"first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288"}],"doi":"10.1007/s10955-022-02965-9","publisher":"Springer Nature","language":[{"iso":"eng"}],"file_date_updated":"2022-08-08T07:36:34Z","type":"journal_article","day":"29","has_accepted_license":"1","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"citation":{"ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022.","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9.","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","apa":"Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9."},"intvolume":" 189","ec_funded":1,"article_number":"5","status":"public","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."}],"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)","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"11732","month":"07","title":"The BCS energy gap at high density","oa":1,"publication_status":"published","article_type":"original"},{"ec_funded":1,"article_number":"122302","status":"public","abstract":[{"lang":"eng","text":"A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential."}],"day":"01","has_accepted_license":"1","intvolume":" 63","citation":{"ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022.","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:10.1063/5.0104675.","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104675.","ista":"Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 63(12), 122302.","apa":"Henheik, S. J., & Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104675","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0104675","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022)."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"12110","month":"12","title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions","oa":1,"publication_status":"published","article_type":"original","department":[{"_id":"LaEr"}],"acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","quality_controlled":"1","date_created":"2023-01-08T23:00:53Z","year":"2022","date_updated":"2023-08-03T14:12:01Z","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"volume":63,"isi":1,"file":[{"content_type":"application/pdf","date_created":"2023-01-20T11:58:59Z","file_id":"12327","success":1,"date_updated":"2023-01-20T11:58:59Z","access_level":"open_access","file_name":"2022_JourMathPhysics_Henheik.pdf","file_size":5436804,"creator":"dernst","relation":"main_file","checksum":"5150287295e0ce4f12462c990744d65d"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","publication_identifier":{"issn":["0022-2488"]},"scopus_import":"1","doi":"10.1063/5.0104675","publisher":"AIP Publishing","language":[{"iso":"eng"}],"file_date_updated":"2023-01-20T11:58:59Z","type":"journal_article","external_id":{"isi":["000900748900002"]},"oa_version":"Published Version","date_published":"2022-12-01T00:00:00Z","publication":"Journal of Mathematical Physics","issue":"12","ddc":["510"],"author":[{"first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Roderich","full_name":"Tumulka, Roderich","last_name":"Tumulka"}]},{"oa":1,"title":"Rank-uniform local law for Wigner matrices","publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"10","_id":"12148","acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","department":[{"_id":"LaEr"}],"article_number":"e96","status":"public","abstract":[{"text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.","lang":"eng"}],"ec_funded":1,"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2022.86.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2022.86","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86."},"intvolume":" 10","day":"27","has_accepted_license":"1","language":[{"iso":"eng"}],"file_date_updated":"2023-01-24T10:02:40Z","type":"journal_article","doi":"10.1017/fms.2022.86","publisher":"Cambridge University Press","publication":"Forum of Mathematics, Sigma","ddc":["510"],"author":[{"last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"oa_version":"Published Version","external_id":{"isi":["000873719200001"]},"date_published":"2022-10-27T00:00:00Z","volume":10,"file":[{"file_name":"2022_ForumMath_Cipolloni.pdf","date_updated":"2023-01-24T10:02:40Z","success":1,"access_level":"open_access","date_created":"2023-01-24T10:02:40Z","content_type":"application/pdf","file_id":"12356","checksum":"94a049aeb1eea5497aa097712a73c400","relation":"main_file","creator":"dernst","file_size":817089}],"isi":1,"quality_controlled":"1","year":"2022","date_created":"2023-01-12T12:07:30Z","date_updated":"2023-08-04T09:00:35Z","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"publication_identifier":{"issn":["2050-5094"]},"scopus_import":"1","article_processing_charge":"No","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"}},{"day":"15","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"citation":{"short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","ama":"Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007","apa":"Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007","ista":"Pitrik J, Virosztek D. 2021. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217.","chicago":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007.","ieee":"J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” Linear Algebra and its Applications, vol. 609. Elsevier, pp. 203–217, 2021.","mla":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2021, pp. 203–17, doi:10.1016/j.laa.2020.09.007."},"intvolume":" 609","ec_funded":1,"status":"public","abstract":[{"lang":"eng","text":"It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim."}],"acknowledgement":"The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum Information Theory, No. 96 141, and by Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","department":[{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"01","_id":"8373","oa":1,"title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","publication_status":"published","article_type":"original","article_processing_charge":"No","publication_identifier":{"issn":["0024-3795"]},"main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"page":"203-217","quality_controlled":"1","date_created":"2020-09-11T08:35:50Z","year":"2021","date_updated":"2023-08-04T10:58:14Z","project":[{"call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"volume":609,"isi":1,"oa_version":"Preprint","external_id":{"isi":["000581730500011"],"arxiv":["2002.11678"]},"date_published":"2021-01-15T00:00:00Z","publication":"Linear Algebra and its Applications","author":[{"full_name":"Pitrik, József","first_name":"József","last_name":"Pitrik"},{"first_name":"Daniel","full_name":"Virosztek, Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511"}],"doi":"10.1016/j.laa.2020.09.007","publisher":"Elsevier","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article"},{"citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2021.","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-020-01003-7","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7."},"day":"01","has_accepted_license":"1","status":"public","abstract":[{"text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.","lang":"eng"}],"ec_funded":1,"department":[{"_id":"LaEr"}],"title":"Edge universality for non-Hermitian random matrices","oa":1,"publication_status":"published","article_type":"original","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"02","_id":"8601","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"isi":1,"file":[{"checksum":"611ae28d6055e1e298d53a57beb05ef4","relation":"main_file","creator":"dernst","file_size":497032,"file_name":"2020_ProbTheory_Cipolloni.pdf","access_level":"open_access","date_updated":"2020-10-05T14:53:40Z","success":1,"content_type":"application/pdf","date_created":"2020-10-05T14:53:40Z","file_id":"8612"}],"quality_controlled":"1","date_created":"2020-10-04T22:01:37Z","year":"2021","date_updated":"2024-03-07T15:07:53Z","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"publication":"Probability Theory and Related Fields","ddc":["510"],"author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"external_id":{"arxiv":["1908.00969"],"isi":["000572724600002"]},"oa_version":"Published Version","date_published":"2021-02-01T00:00:00Z","language":[{"iso":"eng"}],"arxiv":1,"file_date_updated":"2020-10-05T14:53:40Z","type":"journal_article","doi":"10.1007/s00440-020-01003-7","publisher":"Springer Nature"},{"author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"}],"ddc":["510"],"date_published":"2021-01-25T00:00:00Z","oa_version":"Published Version","type":"dissertation","file_date_updated":"2021-01-25T14:19:10Z","language":[{"iso":"eng"}],"publisher":"Institute of Science and Technology Austria","doi":"10.15479/AT:ISTA:9022","publication_identifier":{"issn":["2663-337X"]},"article_processing_charge":"No","file":[{"date_created":"2021-01-25T14:19:03Z","content_type":"application/pdf","file_id":"9043","success":1,"access_level":"open_access","date_updated":"2021-01-25T14:19:03Z","file_name":"thesis.pdf","file_size":4127796,"creator":"gcipollo","relation":"main_file","checksum":"5a93658a5f19478372523ee232887e2b"},{"date_created":"2021-01-25T14:19:10Z","file_id":"9044","content_type":"application/zip","date_updated":"2021-01-25T14:19:10Z","access_level":"closed","file_name":"Thesis_files.zip","file_size":12775206,"creator":"gcipollo","relation":"source_file","checksum":"e8270eddfe6a988e92a53c88d1d19b8c"}],"project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"date_updated":"2023-09-07T13:29:32Z","year":"2021","date_created":"2021-01-21T18:16:54Z","page":"380","alternative_title":["ISTA Thesis"],"acknowledgement":"I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"publication_status":"published","oa":1,"title":"Fluctuations in the spectrum of random matrices","_id":"9022","month":"01","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","mla":"Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022.","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022.","apa":"Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022"},"supervisor":[{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"has_accepted_license":"1","day":"25","abstract":[{"lang":"eng","text":"In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices."}],"status":"public","ec_funded":1,"degree_awarded":"PhD"},{"keyword":["General Mathematics"],"citation":{"ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021.","mla":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.","chicago":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595.","apa":"Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595.","ama":"Virosztek D. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595","short":"D. Virosztek, Advances in Mathematics 380 (2021)."},"intvolume":" 380","day":"26","status":"public","article_number":"107595","abstract":[{"lang":"eng","text":"In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space."}],"ec_funded":1,"department":[{"_id":"LaEr"}],"acknowledgement":"D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","publication_status":"published","title":"The metric property of the quantum Jensen-Shannon divergence","oa":1,"article_type":"original","month":"03","_id":"9036","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["0001-8708"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.10447"}],"article_processing_charge":"No","isi":1,"volume":380,"date_created":"2021-01-22T17:55:17Z","year":"2021","quality_controlled":"1","project":[{"name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"date_updated":"2023-08-07T13:34:48Z","publication":"Advances in Mathematics","issue":"3","author":[{"full_name":"Virosztek, Daniel","first_name":"Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Preprint","external_id":{"isi":["000619676100035"],"arxiv":["1910.10447"]},"date_published":"2021-03-26T00:00:00Z","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","doi":"10.1016/j.aim.2021.107595","publisher":"Elsevier"},{"main_file_link":[{"url":"https://arxiv.org/abs/2103.04817","open_access":"1"}],"citation":{"apa":"Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817","ista":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817.","chicago":"Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.04817.","mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817.","ieee":"L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” arXiv. .","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","ama":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817"},"day":"08","article_processing_charge":"No","article_number":"2103.04817","status":"public","abstract":[{"lang":"eng","text":"We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.\r\nIt is shown that the deterministic level of the maximum interpolates smoothly between the ones\r\nof log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of\r\nlog-correlated variables with time-dependent variance and rate occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian correction. This correction is expected to be present for the\r\nRiemann zeta function and pertains to the question of the correct order of the maximum of\r\nthe zeta function in large intervals."}],"year":"2021","date_created":"2021-03-09T11:08:15Z","date_updated":"2023-05-03T10:22:59Z","ec_funded":1,"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"publication":"arXiv","author":[{"first_name":"Louis-Pierre","full_name":"Arguin, Louis-Pierre","last_name":"Arguin"},{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","last_name":"Dubach","first_name":"Guillaume","full_name":"Dubach, Guillaume"},{"last_name":"Hartung","full_name":"Hartung, Lisa","first_name":"Lisa"}],"oa_version":"Preprint","external_id":{"arxiv":["2103.04817"]},"date_published":"2021-03-08T00:00:00Z","department":[{"_id":"LaEr"}],"acknowledgement":"The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099.","oa":1,"title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","language":[{"iso":"eng"}],"publication_status":"submitted","arxiv":1,"type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9230","month":"03","doi":"10.48550/arXiv.2103.04817"}]