LOCAL LAW AND TRACY-WIDOM LIMIT FOR SPARSE SAMPLE COVARIANCE MATRICES

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dc.contributor.authorHwang, Jong Yunko
dc.contributor.authorLee, Ji Oonko
dc.contributor.authorSchnelli, Kevinko
dc.date.accessioned2019-11-04T06:20:31Z-
dc.date.available2019-11-04T06:20:31Z-
dc.date.created2019-11-04-
dc.date.created2019-11-04-
dc.date.issued2019-10-
dc.identifier.citationANNALS OF APPLIED PROBABILITY, v.29, no.5, pp.3006 - 3036-
dc.identifier.issn1050-5164-
dc.identifier.urihttp://hdl.handle.net/10203/268206-
dc.description.abstractWe consider spectral properties of sparse sample covariance matrices, which includes biadjacency matrices of the bipartite Erdos-Renyi graph model. We prove a local law for the eigenvalue density up to the upper spectral edge. Under a suitable condition on the sparsity, we also prove that the limiting distribution of the rescaled, shifted extremal eigenvalues is given by the GOE Tracy-Widom law with an explicit formula on the deterministic shift of the spectral edge. For the biadjacency matrix of an Erdos-Renyi graph with two vertex sets of comparable sizes M and N, this establishes Tracy-Widom fluctuations of the second largest eigenvalue when the connection probability p is much larger than N-2/3 with a deterministic shift of order (Np)(-1).-
dc.languageEnglish-
dc.publisherINST MATHEMATICAL STATISTICS-
dc.titleLOCAL LAW AND TRACY-WIDOM LIMIT FOR SPARSE SAMPLE COVARIANCE MATRICES-
dc.typeArticle-
dc.identifier.wosid000491159000011-
dc.identifier.scopusid2-s2.0-85075059742-
dc.type.rimsART-
dc.citation.volume29-
dc.citation.issue5-
dc.citation.beginningpage3006-
dc.citation.endingpage3036-
dc.citation.publicationnameANNALS OF APPLIED PROBABILITY-
dc.identifier.doi10.1214/19-AAP1472-
dc.contributor.localauthorLee, Ji Oon-
dc.contributor.nonIdAuthorSchnelli, Kevin-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorHigh-dimensional sample covariance matrices-
dc.subject.keywordAuthorlocal law-
dc.subject.keywordAuthorTracy-Widom distribution-
dc.subject.keywordPlusLARGEST EIGENVALUE-
dc.subject.keywordPlusSPECTRAL STATISTICS-
dc.subject.keywordPlusEDGE UNIVERSALITY-
dc.subject.keywordPlusCOMPONENTS-
dc.subject.keywordPlusNUMBER-
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