变形Wigner矩阵的体通用性

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Probability Pub Date : 2014-05-26 DOI:10.1214/15-AOP1023

J. Lee, Kevin Schnelli, Ben Stetler, H. Yau

{"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}

引用次数: 74

摘要

我们考虑N×N随机矩阵H=W+V的形式，其中W是一个实对称或复厄米维格纳矩阵，V是一个随机的或确定的，实的，对角矩阵，其元素与W无关。我们假设W的矩阵元素呈次指数衰减，我们选择V，使W和V的特征值通常具有相同的阶。对于一大类对角矩阵V，我们证明了在大N的极限下，大部分谱中的局部统计量是全称的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Bulk universality for deformed Wigner matrices

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

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.