{"title":"变形Wigner矩阵的体通用性","authors":"J. Lee, Kevin Schnelli, Ben Stetler, H. Yau","doi":"10.1214/15-AOP1023","DOIUrl":null,"url":null,"abstract":"We consider N×N random matrices of the form H=W+V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.","PeriodicalId":50763,"journal":{"name":"Annals of Probability","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2014-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"74","resultStr":"{\"title\":\"Bulk universality for deformed Wigner matrices\",\"authors\":\"J. Lee, Kevin Schnelli, Ben Stetler, H. Yau\",\"doi\":\"10.1214/15-AOP1023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider N×N random matrices of the form H=W+V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.\",\"PeriodicalId\":50763,\"journal\":{\"name\":\"Annals of Probability\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2014-05-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"74\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Probability\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/15-AOP1023\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/15-AOP1023","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
We consider N×N random matrices of the form H=W+V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the local statistics in the bulk of the spectrum are universal in the limit of large N.
期刊介绍：
The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.
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