[{"doi":"10.1214/23-aop1643","_id":"14849","article_type":"original","ec_funded":1,"acknowledgement":"The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation.","year":"2023","date_created":"2024-01-22T08:08:41Z","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2023;51(6):2192-2242. doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>.","mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>"},"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"publisher":"Institute of Mathematical Statistics","date_published":"2023-11-01T00:00:00Z","page":"2192-2242","department":[{"_id":"LaEr"}],"quality_controlled":"1","volume":51,"project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"external_id":{"arxiv":["2206.04448"]},"abstract":[{"text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.","lang":"eng"}],"publication_status":"published","publication":"The Annals of Probability","language":[{"iso":"eng"}],"intvolume":"        51","oa":1,"date_updated":"2024-01-23T10:56:30Z","article_processing_charge":"No","issue":"6","title":"On the rightmost eigenvalue of non-Hermitian random matrices","status":"public","type":"journal_article","publication_identifier":{"issn":["0091-1798"]},"month":"11","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Yuanyuan","full_name":"Xu, Yuanyuan","last_name":"Xu"}],"arxiv":1},{"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"month":"03","day":"01","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1811.11598"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo"}],"arxiv":1,"status":"public","type":"journal_article","isi":1,"intvolume":"        50","scopus_import":"1","oa":1,"date_updated":"2023-10-17T12:50:24Z","issue":"2","article_processing_charge":"No","title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","publication":"Annals of Probability","language":[{"iso":"eng"}],"external_id":{"isi":["000773518500005"],"arxiv":["1811.11598"]},"abstract":[{"text":"We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.","lang":"eng"}],"publication_status":"published","publisher":"Institute of Mathematical Statistics","date_published":"2022-03-01T00:00:00Z","page":"591-648","department":[{"_id":"JaMa"}],"volume":50,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"ec_funded":1,"acknowledgement":"Research supported by the Sonderforschungsbereich 1060 and the Hausdorff Center for Mathematics. The author gratefully acknowledges funding of his current position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr. Jan Maas).","year":"2022","citation":{"apa":"Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1541\">https://doi.org/10.1214/21-AOP1541</a>","chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1541\">https://doi.org/10.1214/21-AOP1541</a>.","mla":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” <i>Annals of Probability</i>, vol. 50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:<a href=\"https://doi.org/10.1214/21-AOP1541\">10.1214/21-AOP1541</a>.","ista":"Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” <i>Annals of Probability</i>, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","ama":"Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. <i>Annals of Probability</i>. 2022;50(2):591-648. doi:<a href=\"https://doi.org/10.1214/21-AOP1541\">10.1214/21-AOP1541</a>"},"date_created":"2022-05-08T22:01:44Z","doi":"10.1214/21-AOP1541","_id":"11354","article_type":"original"},{"isi":1,"scopus_import":"1","intvolume":"        50","article_processing_charge":"No","issue":"3","date_updated":"2023-08-03T07:16:53Z","oa":1,"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","publication":"Annals of Probability","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"month":"05","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"oa_version":"Preprint","arxiv":1,"author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"status":"public","type":"journal_article","year":"2022","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.","date_created":"2022-05-29T22:01:53Z","citation":{"mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>.","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.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” <i>Annals of Probability</i>, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. 2022;50(3):984-1012. doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>"},"doi":"10.1214/21-AOP1552","article_type":"original","_id":"11418","abstract":[{"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).","lang":"eng"}],"external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"publication_status":"published","date_published":"2022-05-01T00:00:00Z","publisher":"Institute of Mathematical Statistics","volume":50,"quality_controlled":"1","department":[{"_id":"LaEr"}],"page":"984-1012"},{"publication_status":"published","external_id":{"isi":["000528269100013"],"arxiv":["1804.07744"]},"abstract":[{"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.","lang":"eng"}],"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"page":"963-1001","department":[{"_id":"LaEr"}],"volume":48,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","date_published":"2020-03-01T00:00:00Z","date_created":"2019-03-28T09:20:08Z","citation":{"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>","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>.","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>.","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.","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>","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001."},"year":"2020","ec_funded":1,"related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"},{"relation":"dissertation_contains","id":"6179","status":"public"}]},"_id":"6184","article_type":"original","doi":"10.1214/19-AOP1379","author":[{"full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"orcid":"0000-0002-4821-3297","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","first_name":"Torben H"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"arxiv":1,"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"day":"01","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"03","publication_identifier":{"issn":["0091-1798"]},"status":"public","type":"journal_article","title":"Correlated random matrices: Band rigidity and edge universality","oa":1,"date_updated":"2024-02-22T14:34:33Z","issue":"2","article_processing_charge":"No","intvolume":"        48","scopus_import":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Annals of Probability"},{"volume":32,"quality_controlled":"1","extern":"1","page":"1-27","status":"public","date_published":"2004-03-04T00:00:00Z","type":"journal_article","publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"04","oa_version":"None","publication_identifier":{"issn":["0091-1798"]},"month":"03","author":[{"first_name":"Leonid","full_name":"Koralov, Leonid","last_name":"Koralov"},{"first_name":"Vadim","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"last_name":"Dolgopyat","first_name":"Dmitry","full_name":"Dolgopyat, Dmitry"}],"publication_status":"published","doi":"10.1214/aop/1078415827","publication":"The Annals of Probability","article_type":"original","_id":"8518","language":[{"iso":"eng"}],"intvolume":"        32","title":"Sample path properties of the stochastic flows","date_created":"2020-09-18T10:49:19Z","citation":{"apa":"Koralov, L., Kaloshin, V., &#38; Dolgopyat, D. (2004). Sample path properties of the stochastic flows. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/aop/1078415827\">https://doi.org/10.1214/aop/1078415827</a>","mla":"Koralov, Leonid, et al. “Sample Path Properties of the Stochastic Flows.” <i>The Annals of Probability</i>, vol. 32, no. 1A, Institute of Mathematical Statistics, 2004, pp. 1–27, doi:<a href=\"https://doi.org/10.1214/aop/1078415827\">10.1214/aop/1078415827</a>.","chicago":"Koralov, Leonid, Vadim Kaloshin, and Dmitry Dolgopyat. “Sample Path Properties of the Stochastic Flows.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2004. <a href=\"https://doi.org/10.1214/aop/1078415827\">https://doi.org/10.1214/aop/1078415827</a>.","ista":"Koralov L, Kaloshin V, Dolgopyat D. 2004. Sample path properties of the stochastic flows. The Annals of Probability. 32(1A), 1–27.","ieee":"L. Koralov, V. Kaloshin, and D. Dolgopyat, “Sample path properties of the stochastic flows,” <i>The Annals of Probability</i>, vol. 32, no. 1A. Institute of Mathematical Statistics, pp. 1–27, 2004.","ama":"Koralov L, Kaloshin V, Dolgopyat D. Sample path properties of the stochastic flows. <i>The Annals of Probability</i>. 2004;32(1A):1-27. doi:<a href=\"https://doi.org/10.1214/aop/1078415827\">10.1214/aop/1078415827</a>","short":"L. Koralov, V. Kaloshin, D. Dolgopyat, The Annals of Probability 32 (2004) 1–27."},"year":"2004","issue":"1A","article_processing_charge":"No","date_updated":"2021-01-12T08:19:50Z"}]