BULK UNIVERSALITY FOR DEFORMED WIGNER MATRICES

• 成果类型: Article
• 署名作者: Lee, Ji Oon; Schnelli, Kevin; Stetler, Ben; Yau, Horng-Tzer
• 署名单位: Korea Advanced Institute of Science & Technology (KAIST); Institute of Science & Technology - Austria; Harvard University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1023
• 发表日期: 2016
• 页码: 2349-2425
• 关键词: gaussian random matrices; large-n limit; external source; semicircle law; Orthogonal polynomials; spectrum edge; asymptotics; eigenvalues; delocalization; distributions

摘要

We consider N x 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.