DC Field | Value | Language |
---|---|---|
dc.contributor.author | Hwang, Jong Yun | ko |
dc.contributor.author | Lee, Ji Oon | ko |
dc.contributor.author | Schnelli, Kevin | ko |
dc.date.accessioned | 2019-11-04T06:20:31Z | - |
dc.date.available | 2019-11-04T06:20:31Z | - |
dc.date.created | 2019-11-04 | - |
dc.date.created | 2019-11-04 | - |
dc.date.issued | 2019-10 | - |
dc.identifier.citation | ANNALS OF APPLIED PROBABILITY, v.29, no.5, pp.3006 - 3036 | - |
dc.identifier.issn | 1050-5164 | - |
dc.identifier.uri | http://hdl.handle.net/10203/268206 | - |
dc.description.abstract | We 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.language | English | - |
dc.publisher | INST MATHEMATICAL STATISTICS | - |
dc.title | LOCAL LAW AND TRACY-WIDOM LIMIT FOR SPARSE SAMPLE COVARIANCE MATRICES | - |
dc.type | Article | - |
dc.identifier.wosid | 000491159000011 | - |
dc.identifier.scopusid | 2-s2.0-85075059742 | - |
dc.type.rims | ART | - |
dc.citation.volume | 29 | - |
dc.citation.issue | 5 | - |
dc.citation.beginningpage | 3006 | - |
dc.citation.endingpage | 3036 | - |
dc.citation.publicationname | ANNALS OF APPLIED PROBABILITY | - |
dc.identifier.doi | 10.1214/19-AAP1472 | - |
dc.contributor.localauthor | Lee, Ji Oon | - |
dc.contributor.nonIdAuthor | Schnelli, Kevin | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | High-dimensional sample covariance matrices | - |
dc.subject.keywordAuthor | local law | - |
dc.subject.keywordAuthor | Tracy-Widom distribution | - |
dc.subject.keywordPlus | LARGEST EIGENVALUE | - |
dc.subject.keywordPlus | SPECTRAL STATISTICS | - |
dc.subject.keywordPlus | EDGE UNIVERSALITY | - |
dc.subject.keywordPlus | COMPONENTS | - |
dc.subject.keywordPlus | NUMBER | - |
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