[{"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Communications on Pure and Applied Mathematics","month":"05","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program"}],"oa_version":"Published Version","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"success":1,"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"14388","file_size":803440,"checksum":"8346bc2642afb4ccb7f38979f41df5d9","date_created":"2023-10-04T09:21:48Z","content_type":"application/pdf","file_name":"2023_CommPureMathematics_Cipolloni.pdf","date_updated":"2023-10-04T09:21:48Z"}],"type":"journal_article","date_published":"2023-05-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png"},"oa":1,"publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"file_date_updated":"2023-10-04T09:21:48Z","quality_controlled":"1","ec_funded":1,"page":"946-1034","article_type":"original","publisher":"Wiley","issue":"5","author":[{"first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"scopus_import":"1","_id":"10405","intvolume":"        76","title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","date_created":"2021-12-05T23:01:41Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","publication_status":"published","ddc":["510"],"volume":76,"acknowledgement":"L.E. would like to thank Nathanaël Berestycki and D.S.would like to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","external_id":{"isi":["000724652500001"],"arxiv":["1912.04100"]},"isi":1,"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2023. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.","ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2023;76(5):946-1034. doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 76(5), 946–1034.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","mla":"Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>."},"year":"2023","date_updated":"2023-10-04T09:22:55Z","abstract":[{"lang":"eng","text":"We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. "}],"day":"01","arxiv":1,"doi":"10.1002/cpa.22028"},{"language":[{"iso":"eng"}],"publication":"Probability Theory and Related Fields","has_accepted_license":"1","month":"02","oa_version":"Published Version","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","file":[{"success":1,"access_level":"open_access","relation":"main_file","file_id":"8612","creator":"dernst","date_created":"2020-10-05T14:53:40Z","checksum":"611ae28d6055e1e298d53a57beb05ef4","file_size":497032,"date_updated":"2020-10-05T14:53:40Z","content_type":"application/pdf","file_name":"2020_ProbTheory_Cipolloni.pdf"}],"date_published":"2021-02-01T00:00:00Z","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)"},"oa":1,"publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"file_date_updated":"2020-10-05T14:53:40Z","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Springer Nature","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"_id":"8601","scopus_import":"1","title":"Edge universality for non-Hermitian random matrices","publication_status":"published","date_created":"2020-10-04T22:01:37Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","ddc":["510"],"isi":1,"external_id":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"date_updated":"2024-03-07T15:07:53Z","year":"2021","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>.","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., &#38; Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021."},"abstract":[{"lang":"eng","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."}],"doi":"10.1007/s00440-020-01003-7","arxiv":1,"day":"01"},{"abstract":[{"lang":"eng","text":"We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge."}],"day":"21","doi":"10.2140/pmp.2021.2.221","arxiv":1,"external_id":{"arxiv":["1907.13631"]},"citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>","ama":"Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. 2021;2(2):221-280. doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","mla":"Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280."},"year":"2021","date_updated":"2024-02-19T08:30:00Z","volume":2,"acknowledgement":"Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn.","intvolume":"         2","title":"Spectral radius of random matrices with independent entries","date_created":"2024-02-18T23:01:03Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","publication_status":"published","issue":"2","author":[{"first_name":"Johannes","last_name":"Alt","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"15013","article_type":"original","publisher":"Mathematical Sciences Publishers","ec_funded":1,"quality_controlled":"1","page":"221-280","oa":1,"publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"type":"journal_article","date_published":"2021-05-21T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1907.13631"}],"month":"05","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"oa_version":"Preprint","publication":"Probability and Mathematical Physics","language":[{"iso":"eng"}]},{"supervisor":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"}],"oa":1,"publication_identifier":{"issn":["2663-337X"]},"date_published":"2021-01-25T00:00:00Z","type":"dissertation","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","file":[{"creator":"gcipollo","file_id":"9043","success":1,"relation":"main_file","access_level":"open_access","file_name":"thesis.pdf","content_type":"application/pdf","date_updated":"2021-01-25T14:19:03Z","file_size":4127796,"checksum":"5a93658a5f19478372523ee232887e2b","date_created":"2021-01-25T14:19:03Z"},{"relation":"source_file","access_level":"closed","creator":"gcipollo","file_id":"9044","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","file_size":12775206,"date_created":"2021-01-25T14:19:10Z","file_name":"Thesis_files.zip","content_type":"application/zip","date_updated":"2021-01-25T14:19:10Z"}],"month":"01","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","grant_number":"665385"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"degree_awarded":"PhD","doi":"10.15479/AT:ISTA:9022","day":"25","date_updated":"2023-09-07T13:29:32Z","citation":{"ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/AT:ISTA:9022\">https://doi.org/10.15479/AT:ISTA:9022</a>.","apa":"Cipolloni, G. (2021). <i>Fluctuations in the spectrum of random matrices</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:9022\">https://doi.org/10.15479/AT:ISTA:9022</a>","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9022\">10.15479/AT:ISTA:9022</a>","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","mla":"Cipolloni, Giorgio. <i>Fluctuations in the Spectrum of Random Matrices</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9022\">10.15479/AT:ISTA:9022</a>.","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021."},"year":"2021","ddc":["510"],"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.","alternative_title":["ISTA Thesis"],"title":"Fluctuations in the spectrum of random matrices","publication_status":"published","article_processing_charge":"No","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_created":"2021-01-21T18:16:54Z","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"}],"_id":"9022","publisher":"Institute of Science and Technology Austria","file_date_updated":"2021-01-25T14:19:10Z","page":"380","ec_funded":1},{"publication_identifier":{"eissn":["20505094"]},"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":"2021-05-27T00:00:00Z","file":[{"access_level":"open_access","relation":"main_file","success":1,"creator":"cziletti","file_id":"9555","file_size":483458,"checksum":"47c986578de132200d41e6d391905519","date_created":"2021-06-15T14:40:45Z","file_name":"2021_ForumMath_Bao.pdf","content_type":"application/pdf","date_updated":"2021-06-15T14:40:45Z"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"oa_version":"Published Version","article_number":"e44","month":"05","has_accepted_license":"1","publication":"Forum of Mathematics, Sigma","language":[{"iso":"eng"}],"day":"27","doi":"10.1017/fms.2021.38","arxiv":1,"abstract":[{"lang":"eng","text":"We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. "}],"citation":{"ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2021). Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e44, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021)."},"year":"2021","date_updated":"2023-08-08T14:03:40Z","external_id":{"isi":["000654960800001"],"arxiv":["2008.07061"]},"isi":1,"acknowledgement":"The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation","volume":9,"ddc":["510"],"date_created":"2021-06-13T22:01:33Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","publication_status":"published","intvolume":"         9","title":"Equipartition principle for Wigner matrices","scopus_import":"1","_id":"9550","author":[{"first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"publisher":"Cambridge University Press","article_type":"original","ec_funded":1,"quality_controlled":"1","file_date_updated":"2021-06-15T14:40:45Z"},{"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Annales Henri Poincaré ","month":"12","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"oa_version":"Published Version","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","file_size":1162454,"date_created":"2022-05-12T12:50:27Z","file_name":"2021_AnnHenriPoincare_Erdoes.pdf","content_type":"application/pdf","date_updated":"2022-05-12T12:50:27Z","access_level":"open_access","success":1,"relation":"main_file","creator":"dernst","file_id":"11365"}],"type":"journal_article","date_published":"2021-12-01T00:00:00Z","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":["1424-0661"],"issn":["1424-0637"]},"file_date_updated":"2022-05-12T12:50:27Z","quality_controlled":"1","ec_funded":1,"page":"4205–4269","article_type":"original","publisher":"Springer Nature","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H"},{"last_name":"Nemish","first_name":"Yuriy","full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"9912","intvolume":"        22","title":"Scattering in quantum dots via noncommutative rational functions","date_created":"2021-08-15T22:01:29Z","article_processing_charge":"Yes (in subscription journal)","department":[{"_id":"LaEr"}],"publication_status":"published","ddc":["510"],"volume":22,"acknowledgement":"The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks.","external_id":{"isi":["000681531500001"],"arxiv":["1911.05112"]},"isi":1,"citation":{"mla":"Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>, vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269.","ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","apa":"Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>","ama":"Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. 2021;22:4205–4269. doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” <i>Annales Henri Poincaré </i>, vol. 22. Springer Nature, pp. 4205–4269, 2021.","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>."},"year":"2021","date_updated":"2023-08-11T10:31:48Z","abstract":[{"text":"In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via 𝑁≪𝑀 channels, the density 𝜌 of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries.","lang":"eng"}],"day":"01","doi":"10.1007/s00023-021-01085-6","arxiv":1},{"language":[{"iso":"eng"}],"keyword":["Analysis"],"publication":"Journal of Functional Analysis","oa_version":"Preprint","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"month":"10","article_number":"108639","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2020-10-15T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0022-1236"]},"oa":1,"quality_controlled":"1","ec_funded":1,"publisher":"Elsevier","article_type":"original","_id":"10862","scopus_import":"1","author":[{"first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"issue":"7","publication_status":"published","date_created":"2022-03-18T10:18:59Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","title":"Spectral rigidity for addition of random matrices at the regular edge","intvolume":"       279","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","volume":279,"date_updated":"2023-08-24T14:08:42Z","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” <i>Journal of Functional Analysis</i>, vol. 279, no. 7. Elsevier, 2020.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. 2020;279(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>, vol. 279, no. 7, 108639, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>."},"year":"2020","isi":1,"external_id":{"arxiv":["1708.01597"],"isi":["000559623200009"]},"doi":"10.1016/j.jfa.2020.108639","arxiv":1,"day":"15","abstract":[{"text":"We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix.","lang":"eng"}]},{"publication":"Journal of Functional Analysis","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","article_number":"108507","month":"07","language":[{"iso":"eng"}],"type":"journal_article","date_published":"2020-07-01T00:00:00Z","publication_identifier":{"issn":["00221236"],"eissn":["10960783"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1804.11340","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","scopus_import":"1","_id":"7512","issue":"12","author":[{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","last_name":"Nemish","first_name":"Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2020-02-23T23:00:36Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","publication_status":"published","intvolume":"       278","title":"Local laws for polynomials of Wigner matrices","ec_funded":1,"quality_controlled":"1","publisher":"Elsevier","article_type":"original","citation":{"ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.","mla":"Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 278, no. 12, 108507, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">10.1016/j.jfa.2020.108507</a>.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 278, no. 12. Elsevier, 2020.","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials of Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">https://doi.org/10.1016/j.jfa.2020.108507</a>.","ama":"Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. <i>Journal of Functional Analysis</i>. 2020;278(12). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">10.1016/j.jfa.2020.108507</a>","apa":"Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2020). Local laws for polynomials of Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">https://doi.org/10.1016/j.jfa.2020.108507</a>"},"year":"2020","date_updated":"2023-08-18T06:36:10Z","external_id":{"arxiv":["1804.11340"],"isi":["000522798900001"]},"isi":1,"day":"01","doi":"10.1016/j.jfa.2020.108507","arxiv":1,"abstract":[{"text":"We consider general self-adjoint polynomials in several independent random matrices whose entries are centered and have the same variance. We show that under certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue density on scales just above the eigenvalue spacing follows the global density of states which is determined by free probability theory. We prove that these conditions hold for general homogeneous polynomials of degree two and for symmetrized products of independent matrices with i.i.d. entries, thus establishing the optimal bulk local law for these classes of ensembles. In particular, we generalize a similar result of Anderson for anticommutator. For more general polynomials our conditions are effectively checkable numerically.","lang":"eng"}],"acknowledgement":"The authors are grateful to Oskari Ajanki for his invaluable help at the initial stage of this project, to Serban Belinschi for useful discussions, to Alexander Tikhomirov for calling our attention to the model example in Section 6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös: Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n","volume":278},{"language":[{"iso":"eng"}],"month":"03","oa_version":"Preprint","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"publication":"Annals of Probability","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"},{"id":"6179","relation":"dissertation_contains","status":"public"}]},"status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1804.07744","open_access":"1"}],"oa":1,"publication_identifier":{"issn":["0091-1798"]},"date_published":"2020-03-01T00:00:00Z","type":"journal_article","article_type":"original","publisher":"Institute of Mathematical Statistics","page":"963-1001","ec_funded":1,"quality_controlled":"1","title":"Correlated random matrices: Band rigidity and edge universality","intvolume":"        48","publication_status":"published","department":[{"_id":"LaEr"}],"date_created":"2019-03-28T09:20:08Z","article_processing_charge":"No","author":[{"full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"issue":"2","_id":"6184","scopus_import":"1","volume":48,"abstract":[{"lang":"eng","text":"We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models."}],"doi":"10.1214/19-AOP1379","arxiv":1,"day":"01","isi":1,"external_id":{"arxiv":["1804.07744"],"isi":["000528269100013"]},"date_updated":"2024-02-22T14:34:33Z","year":"2020","citation":{"ista":"Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.","mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” <i>Annals of Probability</i>, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:<a href=\"https://doi.org/10.1214/19-AOP1379\">10.1214/19-AOP1379</a>.","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2020. <a href=\"https://doi.org/10.1214/19-AOP1379\">https://doi.org/10.1214/19-AOP1379</a>.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” <i>Annals of Probability</i>, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.","ama":"Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. <i>Annals of Probability</i>. 2020;48(2):963-1001. doi:<a href=\"https://doi.org/10.1214/19-AOP1379\">10.1214/19-AOP1379</a>","apa":"Alt, J., Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/19-AOP1379\">https://doi.org/10.1214/19-AOP1379</a>"}},{"page":"1203-1278","quality_controlled":"1","ec_funded":1,"file_date_updated":"2020-11-18T11:14:37Z","publisher":"Springer Nature","article_type":"original","_id":"6185","scopus_import":"1","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-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"}],"publication_status":"published","date_created":"2019-03-28T10:21:15Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","intvolume":"       378","volume":378,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work.","ddc":["530","510"],"date_updated":"2023-09-07T12:54:12Z","year":"2020","citation":{"chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” <i>Communications in Mathematical Physics</i>, vol. 378. Springer Nature, pp. 1203–1278, 2020.","ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. 2020;378:1203-1278. doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>","ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>."},"isi":1,"external_id":{"isi":["000529483000001"],"arxiv":["1809.03971"]},"doi":"10.1007/s00220-019-03657-4","arxiv":1,"day":"01","abstract":[{"text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).","lang":"eng"}],"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","has_accepted_license":"1","oa_version":"Published Version","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"month":"09","file":[{"date_created":"2020-11-18T11:14:37Z","file_size":2904574,"checksum":"c3a683e2afdcea27afa6880b01e53dc2","date_updated":"2020-11-18T11:14:37Z","file_name":"2020_CommMathPhysics_Erdoes.pdf","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"8771","creator":"dernst"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","related_material":{"record":[{"status":"public","id":"6179","relation":"dissertation_contains"}]},"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":"2020-09-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa":1},{"publication_identifier":{"eissn":["20103271"],"issn":["20103263"]},"oa":1,"date_published":"2020-07-01T00:00:00Z","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/1806.08751","open_access":"1"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"month":"07","article_number":"2050006","publication":"Random Matrices: Theory and Application","language":[{"iso":"eng"}],"arxiv":1,"doi":"10.1142/S2010326320500069","day":"01","abstract":[{"lang":"eng","text":"We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish."}],"date_updated":"2023-08-28T08:38:48Z","citation":{"mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>.","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","ista":"Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006.","ama":"Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. 2020;9(3). doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>","apa":"Cipolloni, G., &#38; Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3. World Scientific Publishing, 2020.","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>. World Scientific Publishing, 2020. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>."},"year":"2020","isi":1,"external_id":{"isi":["000547464400001"],"arxiv":["1806.08751"]},"volume":9,"publication_status":"published","date_created":"2019-05-26T21:59:14Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","intvolume":"         9","_id":"6488","scopus_import":"1","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","last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"}],"issue":"3","publisher":"World Scientific Publishing","article_type":"original","ec_funded":1,"quality_controlled":"1"},{"acknowledgement":"Partially supported by ERC Advanced Grant No. 338804. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 66538","volume":1,"abstract":[{"text":"We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).","lang":"eng"}],"day":"16","arxiv":1,"doi":"10.2140/pmp.2020.1.101","external_id":{"arxiv":["1908.01653"]},"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. 2020;1(1):101-146. doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics 1 (2020) 101–146.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 1(1), 101–146."},"year":"2020","date_updated":"2024-03-04T10:33:15Z","article_type":"original","publisher":"Mathematical Sciences Publishers","quality_controlled":"1","ec_funded":1,"page":"101-146","intvolume":"         1","title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","article_processing_charge":"No","date_created":"2024-03-04T10:27:57Z","department":[{"_id":"LaEr"}],"publication_status":"published","issue":"1","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","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"15063","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1908.01653","open_access":"1"}],"oa":1,"publication_identifier":{"issn":["2690-1005","2690-0998"]},"type":"journal_article","date_published":"2020-11-16T00:00:00Z","keyword":["General Medicine"],"language":[{"iso":"eng"}],"month":"11","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"oa_version":"Preprint","publication":"Probability and Mathematical Physics"},{"main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","date_published":"2020-11-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["00217670"],"eissn":["15658538"]},"oa":1,"language":[{"iso":"eng"}],"publication":"Journal d'Analyse Mathematique","oa_version":"Preprint","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"month":"11","volume":142,"acknowledgement":"Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195.","date_updated":"2023-08-24T11:16:03Z","citation":{"ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.","mla":"Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>, vol. 142, Springer Nature, 2020, pp. 323–48, doi:<a href=\"https://doi.org/10.1007/s11854-020-0135-2\">10.1007/s11854-020-0135-2</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” <i>Journal d’Analyse Mathematique</i>, vol. 142. Springer Nature, pp. 323–348, 2020.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11854-020-0135-2\">https://doi.org/10.1007/s11854-020-0135-2</a>.","ama":"Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. 2020;142:323-348. doi:<a href=\"https://doi.org/10.1007/s11854-020-0135-2\">10.1007/s11854-020-0135-2</a>","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11854-020-0135-2\">https://doi.org/10.1007/s11854-020-0135-2</a>"},"year":"2020","isi":1,"external_id":{"arxiv":["1804.11199"],"isi":["000611879400008"]},"arxiv":1,"doi":"10.1007/s11854-020-0135-2","day":"01","abstract":[{"text":"We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν have power law behavior with exponents between −1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5].","lang":"eng"}],"page":"323-348","ec_funded":1,"quality_controlled":"1","publisher":"Springer Nature","article_type":"original","_id":"9104","scopus_import":"1","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","first_name":"Zhigang","last_name":"Bao"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","first_name":"Kevin","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231"}],"publication_status":"published","department":[{"_id":"LaEr"}],"date_created":"2021-02-07T23:01:15Z","article_processing_charge":"No","title":"On the support of the free additive convolution","intvolume":"       142"},{"conference":{"end_date":"2019-07-05","location":"Ljubljana, Slovenia","name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics","start_date":"2019-07-01"},"language":[{"iso":"eng"}],"article_number":"34","month":"07","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"oa_version":"Preprint","publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.08750"}],"oa":1,"type":"conference","date_published":"2019-07-01T00:00:00Z","publisher":"Formal Power Series and Algebraic Combinatorics","quality_controlled":"1","ec_funded":1,"title":"New edge asymptotics of skew Young diagrams via free boundaries","date_created":"2020-07-26T22:01:04Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"full_name":"Betea, Dan","last_name":"Betea","first_name":"Dan"},{"full_name":"Bouttier, Jérémie","last_name":"Bouttier","first_name":"Jérémie"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter","first_name":"Peter","last_name":"Nejjar"},{"last_name":"Vuletíc","first_name":"Mirjana","full_name":"Vuletíc, Mirjana"}],"scopus_import":"1","_id":"8175","acknowledgement":"D.B. is especially grateful to Patrik Ferrari for suggesting simplifications in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models of Section 2.\r\n","abstract":[{"lang":"eng","text":"We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices."}],"day":"01","arxiv":1,"external_id":{"arxiv":["1902.08750"]},"citation":{"ama":"Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. In: <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Formal Power Series and Algebraic Combinatorics; 2019.","apa":"Betea, D., Bouttier, J., Nejjar, P., &#38; Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics.","chicago":"Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” In <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Formal Power Series and Algebraic Combinatorics, 2019.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>, Ljubljana, Slovenia, 2019.","mla":"Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>, 34, Formal Power Series and Algebraic Combinatorics, 2019.","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.","ista":"Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew Young diagrams via free boundaries. Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics, 34."},"year":"2019","date_updated":"2021-01-12T08:17:18Z"},{"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","month":"09","oa_version":"Preprint","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"language":[{"iso":"eng"}],"date_published":"2019-09-25T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"issn":["0246-0203"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}],"author":[{"full_name":"Ferrari, Patrick","last_name":"Ferrari","first_name":"Patrick"},{"full_name":"Ghosal, Promit","last_name":"Ghosal","first_name":"Promit"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter","first_name":"Peter","last_name":"Nejjar"}],"issue":"3","_id":"72","scopus_import":"1","title":"Limit law of a second class particle in TASEP with non-random initial condition","intvolume":"        55","publication_status":"published","date_created":"2018-12-11T11:44:29Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"article_processing_charge":"No","page":"1203-1225","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Institute of Mathematical Statistics","isi":1,"external_id":{"arxiv":["1710.02323"],"isi":["000487763200001"]},"date_updated":"2023-10-17T08:53:45Z","citation":{"ista":"Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 55(3), 1203–1225.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>.","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2019;55(3):1203-1225. doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>","apa":"Ferrari, P., Ghosal, P., &#38; Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>"},"year":"2019","abstract":[{"lang":"eng","text":"We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ&lt;λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t."}],"arxiv":1,"doi":"10.1214/18-AIHP916","day":"25","volume":55},{"type":"dissertation","date_published":"2019-03-18T00:00:00Z","oa":1,"supervisor":[{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"publication_identifier":{"issn":["2663-337X"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"1144"},{"status":"public","id":"6186","relation":"part_of_dissertation"},{"status":"public","id":"6185","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"6182"},{"id":"1012","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"6184"}]},"file":[{"date_updated":"2020-07-14T12:47:21Z","content_type":"application/x-gzip","file_name":"2019_Schroeder_Thesis.tar.gz","date_created":"2019-03-28T08:53:52Z","checksum":"6926f66f28079a81c4937e3764be00fc","file_size":7104482,"file_id":"6180","creator":"dernst","access_level":"closed","relation":"source_file"},{"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"6181","checksum":"7d0ebb8d1207e89768cdd497a5bf80fb","file_size":4228794,"date_created":"2019-03-28T08:53:52Z","content_type":"application/pdf","file_name":"2019_Schroeder_Thesis.pdf","date_updated":"2020-07-14T12:47:21Z"}],"has_accepted_license":"1","month":"03","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"oa_version":"Published Version","language":[{"iso":"eng"}],"citation":{"ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria.","short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","mla":"Schröder, Dominik J. <i>From Dyson to Pearcey: Universal Statistics in Random Matrix Theory</i>. Institute of Science and Technology Austria, 2019, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">10.15479/AT:ISTA:th6179</a>.","chicago":"Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random Matrix Theory.” Institute of Science and Technology Austria, 2019. <a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">https://doi.org/10.15479/AT:ISTA:th6179</a>.","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019.","apa":"Schröder, D. J. (2019). <i>From Dyson to Pearcey: Universal statistics in random matrix theory</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">https://doi.org/10.15479/AT:ISTA:th6179</a>","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">10.15479/AT:ISTA:th6179</a>"},"year":"2019","date_updated":"2024-02-22T14:34:33Z","abstract":[{"lang":"eng","text":"In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.\r\nIn the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime.\r\nIn the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure."}],"day":"18","degree_awarded":"PhD","doi":"10.15479/AT:ISTA:th6179","ddc":["515","519"],"author":[{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"_id":"6179","title":"From Dyson to Pearcey: Universal statistics in random matrix theory","alternative_title":["ISTA Thesis"],"article_processing_charge":"No","date_created":"2019-03-28T08:58:59Z","department":[{"_id":"LaEr"}],"publication_status":"published","file_date_updated":"2020-07-14T12:47:21Z","ec_funded":1,"page":"375","publisher":"Institute of Science and Technology Austria"},{"_id":"6182","scopus_import":"1","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","article_processing_charge":"No","date_created":"2019-03-28T09:05:23Z","department":[{"_id":"LaEr"}],"title":"Random matrices with slow correlation decay","intvolume":"         7","ec_funded":1,"quality_controlled":"1","file_date_updated":"2020-07-14T12:47:22Z","publisher":"Cambridge University Press","article_type":"original","date_updated":"2023-09-07T12:54:12Z","citation":{"ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>, vol. 7, e8, Cambridge University Press, 2019, doi:<a href=\"https://doi.org/10.1017/fms.2019.2\">10.1017/fms.2019.2</a>.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” <i>Forum of Mathematics, Sigma</i>, vol. 7. Cambridge University Press, 2019.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2019. <a href=\"https://doi.org/10.1017/fms.2019.2\">https://doi.org/10.1017/fms.2019.2</a>.","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2019.2\">https://doi.org/10.1017/fms.2019.2</a>","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. 2019;7. doi:<a href=\"https://doi.org/10.1017/fms.2019.2\">10.1017/fms.2019.2</a>"},"year":"2019","isi":1,"external_id":{"isi":["000488847100001"],"arxiv":["1705.10661"]},"arxiv":1,"doi":"10.1017/fms.2019.2","day":"26","abstract":[{"lang":"eng","text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."}],"volume":7,"ddc":["510"],"publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","oa_version":"Published Version","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"month":"03","article_number":"e8","language":[{"iso":"eng"}],"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":"2019-03-26T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["20505094"]},"oa":1,"file":[{"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"6883","file_size":1520344,"checksum":"933a472568221c73b2c3ce8c87bf6d15","date_created":"2019-09-17T14:24:13Z","content_type":"application/pdf","file_name":"2019_Forum_Erdoes.pdf","date_updated":"2020-07-14T12:47:22Z"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","related_material":{"record":[{"id":"6179","relation":"dissertation_contains","status":"public"}]}},{"language":[{"iso":"eng"}],"publication":"Pure and Applied Analysis ","oa_version":"Preprint","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"month":"10","main_file_link":[{"url":"https://arxiv.org/abs/1811.04055","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","related_material":{"record":[{"id":"6179","relation":"dissertation_contains","status":"public"}]},"date_published":"2019-10-12T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"oa":1,"page":"615–707","quality_controlled":"1","ec_funded":1,"publisher":"MSP","article_type":"original","_id":"6186","author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"issue":"4","publication_status":"published","date_created":"2019-03-28T10:21:17Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","title":"Cusp universality for random matrices, II: The real symmetric case","intvolume":"         1","volume":1,"date_updated":"2023-09-07T12:54:12Z","year":"2019","citation":{"ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” <i>Pure and Applied Analysis </i>, vol. 1, no. 4. MSP, pp. 615–707, 2019.","chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” <i>Pure and Applied Analysis </i>. MSP, 2019. <a href=\"https://doi.org/10.2140/paa.2019.1.615\">https://doi.org/10.2140/paa.2019.1.615</a>.","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. <i>Pure and Applied Analysis </i>. 2019;1(4):615–707. doi:<a href=\"https://doi.org/10.2140/paa.2019.1.615\">10.2140/paa.2019.1.615</a>","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. <i>Pure and Applied Analysis </i>. MSP. <a href=\"https://doi.org/10.2140/paa.2019.1.615\">https://doi.org/10.2140/paa.2019.1.615</a>","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” <i>Pure and Applied Analysis </i>, vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:<a href=\"https://doi.org/10.2140/paa.2019.1.615\">10.2140/paa.2019.1.615</a>.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis  1 (2019) 615–707."},"external_id":{"arxiv":["1811.04055"]},"arxiv":1,"doi":"10.2140/paa.2019.1.615","day":"12","abstract":[{"text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion.","lang":"eng"}]},{"external_id":{"isi":["000467793600003"],"arxiv":["1706.08343"]},"isi":1,"year":"2019","citation":{"apa":"Alt, J., Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. <i>Annales de l’institut Henri Poincare</i>. Institut Henri Poincaré. <a href=\"https://doi.org/10.1214/18-AIHP894\">https://doi.org/10.1214/18-AIHP894</a>","ama":"Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. <i>Annales de l’institut Henri Poincare</i>. 2019;55(2):661-696. doi:<a href=\"https://doi.org/10.1214/18-AIHP894\">10.1214/18-AIHP894</a>","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” <i>Annales de l’institut Henri Poincare</i>. Institut Henri Poincaré, 2019. <a href=\"https://doi.org/10.1214/18-AIHP894\">https://doi.org/10.1214/18-AIHP894</a>.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” <i>Annales de l’institut Henri Poincare</i>, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.","mla":"Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” <i>Annales de l’institut Henri Poincare</i>, vol. 55, no. 2, Institut Henri Poincaré, 2019, pp. 661–96, doi:<a href=\"https://doi.org/10.1214/18-AIHP894\">10.1214/18-AIHP894</a>.","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.","ista":"Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696."},"date_updated":"2023-10-17T12:20:20Z","abstract":[{"lang":"eng","text":"For a general class of large non-Hermitian random block matrices X we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of X as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers a unified treatment of many structured matrix ensembles."}],"day":"01","doi":"10.1214/18-AIHP894","arxiv":1,"volume":55,"issue":"2","author":[{"full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy","first_name":"Yuriy","last_name":"Nemish"}],"scopus_import":"1","_id":"6240","intvolume":"        55","title":"Location of the spectrum of Kronecker random matrices","date_created":"2019-04-08T14:05:04Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"publication_status":"published","ec_funded":1,"quality_controlled":"1","page":"661-696","publisher":"Institut Henri Poincaré","type":"journal_article","date_published":"2019-05-01T00:00:00Z","oa":1,"publication_identifier":{"issn":["0246-0203"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","related_material":{"record":[{"relation":"dissertation_contains","id":"149","status":"public"}]},"main_file_link":[{"url":"https://arxiv.org/abs/1706.08343","open_access":"1"}],"publication":"Annales de l'institut Henri Poincare","month":"05","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","language":[{"iso":"eng"}]},{"oa":1,"publication_identifier":{"issn":["00911798"]},"date_published":"2019-05-01T00:00:00Z","type":"journal_article","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.05920"}],"month":"05","oa_version":"Preprint","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"publication":"Annals of Probability","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N−1/2+ε and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N)."}],"doi":"10.1214/18-AOP1284","arxiv":1,"day":"01","isi":1,"external_id":{"isi":["000466616100003"],"arxiv":["1612.05920"]},"date_updated":"2023-08-28T09:32:29Z","citation":{"ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. <i>Annals of Probability</i>. 2019;47(3):1270-1334. doi:<a href=\"https://doi.org/10.1214/18-AOP1284\">10.1214/18-AOP1284</a>","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2019). Local single ring theorem on optimal scale. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AOP1284\">https://doi.org/10.1214/18-AOP1284</a>","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” <i>Annals of Probability</i>, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AOP1284\">https://doi.org/10.1214/18-AOP1284</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.","mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” <i>Annals of Probability</i>, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:<a href=\"https://doi.org/10.1214/18-AOP1284\">10.1214/18-AOP1284</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334."},"year":"2019","volume":47,"title":"Local single ring theorem on optimal scale","intvolume":"        47","publication_status":"published","department":[{"_id":"LaEr"}],"article_processing_charge":"No","date_created":"2019-06-02T21:59:13Z","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","first_name":"Zhigang","last_name":"Bao"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"issue":"3","_id":"6511","scopus_import":"1","publisher":"Institute of Mathematical Statistics","page":"1270-1334","quality_controlled":"1","ec_funded":1}]