{"oa":1,"oa_version":"Published Version","date_created":"2024-01-10T09:29:25Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Elsevier","quality_controlled":"1","title":"Spiked multiplicative random matrices and principal components","status":"public","file":[{"content_type":"application/pdf","file_name":"2023_StochasticProcAppl_Ding.pdf","access_level":"open_access","creator":"dernst","relation":"main_file","checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","file_id":"14806","success":1,"date_created":"2024-01-16T08:47:31Z","file_size":1870349,"date_updated":"2024-01-16T08:47:31Z"}],"type":"journal_article","day":"01","article_processing_charge":"Yes (in subscription journal)","month":"09","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2024-01-16T08:49:51Z","date_published":"2023-09-01T00:00:00Z","publication_status":"published","department":[{"_id":"LaEr"}],"abstract":[{"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.","lang":"eng"}],"intvolume":"       163","volume":163,"year":"2023","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.","isi":1,"keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"file_date_updated":"2024-01-16T08:47:31Z","ddc":["510"],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"page":"25-60","doi":"10.1016/j.spa.2023.05.009","publication":"Stochastic Processes and their Applications","has_accepted_license":"1","author":[{"last_name":"Ding","first_name":"Xiucai","full_name":"Ding, Xiucai"},{"last_name":"Ji","first_name":"Hong Chang","full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"external_id":{"arxiv":["2302.13502"],"isi":["001113615900001"]},"publication_identifier":{"eissn":["1879-209X"],"issn":["0304-4149"]},"ec_funded":1,"citation":{"short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and their Applications</i>. 2023;163:25-60. doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>.","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60.","apa":"Ding, X., &#38; Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” <i>Stochastic Processes and their Applications</i>, vol. 163. Elsevier, pp. 25–60, 2023.","mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>, vol. 163, Elsevier, 2023, pp. 25–60, doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>."},"article_type":"original","language":[{"iso":"eng"}],"_id":"14780"}