[{"type":"journal_article","issue":"4","abstract":[{"text":"For large dimensional non-Hermitian random matrices X with real or complex independent, identically distributed, centered entries, we consider the fluctuations of f (X) as a matrix where f is an analytic function around the spectrum of X. We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of A. We find a new formula for the variance of the traceless part that involves the Frobenius norm of A and the L2-norm of f on the boundary of the limiting spectrum. ","lang":"eng"},{"lang":"fre","text":"On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction analytique sur un domaine qui contient le spectre de X. On prouve que, pour une matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie pour la variance de la composante de trace nulle, qui fait intervenir la norme de Frobenius de A et la norme L2 de f sur la frontière du spectre limite."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14667","intvolume":" 59","status":"public","title":"Functional CLT for non-Hermitian random matrices","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"ista":"Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.","ieee":"L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.","apa":"Erdös, L., & Ji, H. C. (2023). Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1304","ama":"Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2023;59(4):2083-2105. doi:10.1214/22-AIHP1304","chicago":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AIHP1304.","mla":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:10.1214/22-AIHP1304.","short":"L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105."},"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","page":"2083-2105","article_type":"original","date_published":"2023-11-01T00:00:00Z","ec_funded":1,"year":"2023","acknowledgement":"The first author was partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated editor for carefully reading this paper and providing helpful comments that improved the quality of the article. Also the authors would like to thank Peter Forrester for pointing out the reference [12] that was absent in the previous version of the manuscript.","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Ji, Hong Chang","last_name":"Ji","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"volume":59,"date_updated":"2023-12-11T12:36:56Z","date_created":"2023-12-10T23:01:00Z","publication_identifier":{"issn":["0246-0203"]},"month":"11","oa":1,"external_id":{"arxiv":["2112.11382"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2112.11382","open_access":"1"}],"project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"quality_controlled":"1","doi":"10.1214/22-AIHP1304","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"doi":"10.1214/22-aap1882","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2010.16083","open_access":"1"}],"external_id":{"arxiv":["2010.16083"]},"publication_identifier":{"issn":["1050-5164"]},"month":"08","volume":33,"date_created":"2024-01-08T13:03:18Z","date_updated":"2024-01-09T08:16:41Z","author":[{"full_name":"Ding, Xiucai","last_name":"Ding","first_name":"Xiucai"},{"last_name":"Ji","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang"}],"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2023","acknowledgement":"The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments.","ec_funded":1,"date_published":"2023-08-01T00:00:00Z","page":"2981-3009","article_type":"original","citation":{"ama":"Ding X, Ji HC. Local laws for multiplication of random matrices. The Annals of Applied Probability. 2023;33(4):2981-3009. doi:10.1214/22-aap1882","ista":"Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009.","ieee":"X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” The Annals of Applied Probability, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023.","apa":"Ding, X., & Ji, H. C. (2023). Local laws for multiplication of random matrices. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1882","mla":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” The Annals of Applied Probability, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:10.1214/22-aap1882.","short":"X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1882."},"publication":"The Annals of Applied Probability","article_processing_charge":"No","day":"01","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"scopus_import":"1","oa_version":"Preprint","intvolume":" 33","title":"Local laws for multiplication of random matrices","status":"public","_id":"14750","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"4","abstract":[{"text":"Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \u0002 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \u0002μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. ","lang":"eng"}],"type":"journal_article"},{"publication_identifier":{"issn":["0304-4149"],"eissn":["1879-209X"]},"month":"09","language":[{"iso":"eng"}],"doi":"10.1016/j.spa.2023.05.009","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"isi":1,"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["001113615900001"],"arxiv":["2302.13502"]},"license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"file_date_updated":"2024-01-16T08:47:31Z","volume":163,"date_created":"2024-01-10T09:29:25Z","date_updated":"2024-01-16T08:49:51Z","author":[{"last_name":"Ding","first_name":"Xiucai","full_name":"Ding, Xiucai"},{"first_name":"Hong Chang","last_name":"Ji","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang"}],"department":[{"_id":"LaEr"}],"publisher":"Elsevier","publication_status":"published","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.","year":"2023","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","day":"01","keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"date_published":"2023-09-01T00:00:00Z","page":"25-60","article_type":"original","citation":{"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.","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.","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60.","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.","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","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"},"publication":"Stochastic Processes and their Applications","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."}],"type":"journal_article","file":[{"checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","success":1,"date_updated":"2024-01-16T08:47:31Z","date_created":"2024-01-16T08:47:31Z","relation":"main_file","file_id":"14806","file_size":1870349,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2023_StochasticProcAppl_Ding.pdf"}],"oa_version":"Published Version","intvolume":" 163","title":"Spiked multiplicative random matrices and principal components","ddc":["510"],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14780"}]