[{"isi":1,"year":"2023","day":"01","publication":"The Annals of Applied Probability","page":"677-725","date_published":"2023-02-01T00:00:00Z","doi":"10.1214/22-aap1826","date_created":"2024-01-10T09:23:31Z","acknowledgement":"K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"citation":{"apa":"Schnelli, K., & Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1826","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 2023;33(1):677-725. doi:10.1214/22-aap1826","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” The Annals of Applied Probability, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023.","short":"K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:10.1214/22-aap1826.","ista":"Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1826."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","full_name":"Xu, Yuanyuan","last_name":"Xu"}],"article_processing_charge":"No","external_id":{"isi":["000946432400021"],"arxiv":["2108.02728"]},"title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"publication_identifier":{"issn":["1050-5164"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":33,"issue":"1","ec_funded":1,"abstract":[{"lang":"eng","text":"We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble."}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2108.02728"}],"month":"02","intvolume":" 33","date_updated":"2024-01-10T13:31:46Z","department":[{"_id":"LaEr"}],"_id":"14775","type":"journal_article","article_type":"original","status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"]},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"article_processing_charge":"Yes (in subscription journal)","external_id":{"arxiv":["2302.13502"],"isi":["001113615900001"]},"author":[{"last_name":"Ding","full_name":"Ding, Xiucai","first_name":"Xiucai"},{"last_name":"Ji","full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang"}],"title":"Spiked multiplicative random matrices and principal components","citation":{"ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 2023;163:25-60. doi:10.1016/j.spa.2023.05.009","apa":"Ding, X., & Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2023.05.009","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” Stochastic Processes and their Applications, vol. 163. Elsevier, pp. 25–60, 2023.","mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” Stochastic Processes and Their Applications, vol. 163, Elsevier, 2023, pp. 25–60, doi:10.1016/j.spa.2023.05.009.","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” Stochastic Processes and Their Applications. Elsevier, 2023. https://doi.org/10.1016/j.spa.2023.05.009."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"quality_controlled":"1","publisher":"Elsevier","acknowledgement":"The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","page":"25-60","date_created":"2024-01-10T09:29:25Z","doi":"10.1016/j.spa.2023.05.009","date_published":"2023-09-01T00:00:00Z","year":"2023","isi":1,"has_accepted_license":"1","publication":"Stochastic Processes and their Applications","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"status":"public","_id":"14780","file_date_updated":"2024-01-16T08:47:31Z","department":[{"_id":"LaEr"}],"date_updated":"2024-01-16T08:49:51Z","ddc":["510"],"intvolume":" 163","month":"09","abstract":[{"lang":"eng","text":"In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix."}],"oa_version":"Published Version","ec_funded":1,"volume":163,"publication_status":"published","publication_identifier":{"issn":["0304-4149"],"eissn":["1879-209X"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2023_StochasticProcAppl_Ding.pdf","date_created":"2024-01-16T08:47:31Z","creator":"dernst","file_size":1870349,"date_updated":"2024-01-16T08:47:31Z","success":1,"checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","file_id":"14806","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}]},{"article_type":"original","type":"journal_article","status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"_id":"14849","department":[{"_id":"LaEr"}],"date_updated":"2024-01-23T10:56:30Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"month":"11","intvolume":" 51","abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","issue":"6","volume":51,"ec_funded":1,"publication_identifier":{"issn":["0091-1798"]},"publication_status":"published","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"},{"full_name":"Xu, Yuanyuan","last_name":"Xu","first_name":"Yuanyuan"}],"external_id":{"arxiv":["2206.04448"]},"article_processing_charge":"No","title":"On the rightmost eigenvalue of non-Hermitian random matrices","citation":{"mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals of Probability, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:10.1214/23-aop1643.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” The Annals of Probability, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 2023;51(6):2192-2242. doi:10.1214/23-aop1643","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-aop1643","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals of Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-aop1643.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":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.","page":"2192-2242","doi":"10.1214/23-aop1643","date_published":"2023-11-01T00:00:00Z","date_created":"2024-01-22T08:08:41Z","year":"2023","day":"01","publication":"The Annals of Probability"},{"month":"01","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2301.01712"}],"oa":1,"oa_version":"Preprint","acknowledgement":"Supported by the ERC Advanced Grant ”RMTBeyond” No. 101020331","abstract":[{"lang":"eng","text":"We prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function $T(z,\\zeta)$ and a general class of related quantities involving two resolvents\r\nat nearby spectral parameters. "}],"date_published":"2023-01-04T00:00:00Z","doi":"10.48550/arXiv.2301.01712","date_created":"2024-03-20T09:41:04Z","ec_funded":1,"day":"04","publication":"arXiv","language":[{"iso":"eng"}],"year":"2023","publication_status":"submitted","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"status":"public","type":"preprint","article_number":"2301.01712","_id":"15128","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"title":"Mesoscopic eigenvalue statistics for Wigner-type matrices","author":[{"first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","last_name":"Riabov"}],"external_id":{"arxiv":["2301.01712"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-03-25T12:48:20Z","citation":{"apa":"Riabov, V. (n.d.). Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. https://doi.org/10.48550/arXiv.2301.01712","ama":"Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. doi:10.48550/arXiv.2301.01712","ieee":"V. Riabov, “Mesoscopic eigenvalue statistics for Wigner-type matrices,” arXiv. .","short":"V. Riabov, ArXiv (n.d.).","mla":"Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, 2301.01712, doi:10.48550/arXiv.2301.01712.","ista":"Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv, 2301.01712.","chicago":"Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2301.01712."}},{"issue":"3","volume":43,"publication_status":"published","publication_identifier":{"eissn":["1095-7162"],"issn":["0895-4798"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.13719"}],"scopus_import":"1","intvolume":" 43","month":"07","abstract":[{"text":"We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146].","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-01-27T06:56:06Z","article_type":"original","type":"journal_article","keyword":["Analysis"],"status":"public","_id":"12179","page":"1469-1487","date_created":"2023-01-12T12:12:38Z","doi":"10.1137/21m1424408","date_published":"2022-07-01T00:00:00Z","year":"2022","publication":"SIAM Journal on Matrix Analysis and Applications","day":"01","oa":1,"publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","article_processing_charge":"No","external_id":{"arxiv":["2105.13719"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"On the condition number of the shifted real Ginibre ensemble","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424408","ama":"Cipolloni G, Erdös L, Schröder DJ. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 2022;43(3):1469-1487. doi:10.1137/21m1424408","mla":"Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:10.1137/21m1424408.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3), 1469–1487.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis and Applications. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424408."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]