DC Field | Value | Language |
---|---|---|
dc.contributor.author | Lee, Ji Oon | ko |
dc.contributor.author | Schnelli, Kevin | ko |
dc.date.accessioned | 2018-06-16T06:35:24Z | - |
dc.date.available | 2018-06-16T06:35:24Z | - |
dc.date.created | 2018-05-28 | - |
dc.date.created | 2018-05-28 | - |
dc.date.created | 2018-05-28 | - |
dc.date.created | 2018-05-28 | - |
dc.date.issued | 2018-06 | - |
dc.identifier.citation | PROBABILITY THEORY AND RELATED FIELDS, v.171, no.1-2, pp.543 - 616 | - |
dc.identifier.issn | 0178-8051 | - |
dc.identifier.uri | http://hdl.handle.net/10203/242403 | - |
dc.description.abstract | We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the ErdAs-R,nyi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy-Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the ErdAs-R,nyi graph this establishes the Tracy-Widom fluctuations of the second largest eigenvalue when p is much larger than wth a deterministic shift of order (Np)(-1).. | - |
dc.language | English | - |
dc.publisher | SPRINGER HEIDELBERG | - |
dc.title | Local law and Tracy-Widom limit for sparse random matrices | - |
dc.type | Article | - |
dc.identifier.wosid | 000432129600012 | - |
dc.identifier.scopusid | 2-s2.0-85020719590 | - |
dc.type.rims | ART | - |
dc.citation.volume | 171 | - |
dc.citation.issue | 1-2 | - |
dc.citation.beginningpage | 543 | - |
dc.citation.endingpage | 616 | - |
dc.citation.publicationname | PROBABILITY THEORY AND RELATED FIELDS | - |
dc.identifier.doi | 10.1007/s00440-017-0787-8 | - |
dc.contributor.localauthor | Lee, Ji Oon | - |
dc.contributor.nonIdAuthor | Schnelli, Kevin | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Local law | - |
dc.subject.keywordAuthor | Sparse random matrices | - |
dc.subject.keywordAuthor | Erdos-Renyi graph | - |
dc.subject.keywordPlus | WIGNER RANDOM MATRICES | - |
dc.subject.keywordPlus | TAILED RANDOM MATRICES | - |
dc.subject.keywordPlus | SEMICIRCLE LAW | - |
dc.subject.keywordPlus | EIGENVALUE STATISTICS | - |
dc.subject.keywordPlus | INDEPENDENT ENTRIES | - |
dc.subject.keywordPlus | SPECTRAL STATISTICS | - |
dc.subject.keywordPlus | BULK UNIVERSALITY | - |
dc.subject.keywordPlus | EDGE | - |
dc.subject.keywordPlus | DELOCALIZATION | - |
dc.subject.keywordPlus | GRAPHS | - |
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