BULK EIGENVALUE STATISTICS FOR RANDOM REGULAR GRAPHS

• 成果类型: Article
• 署名作者: Bauerschmidt, Roland; Huang, Jiaoyang; Knowles, Antti; Yau, Horng-Tzer
• 署名单位: University of Cambridge; Harvard University; University of Geneva
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1145
• 发表日期: 2017
• 页码: 3626-3663
• 关键词: generalized wigner; spectral statistics; UNIVERSALITY; matrices; asymptotics; POLYNOMIALS; gap

摘要

We consider the uniform random d-regular graph on N vertices, with d is an element of [N-alpha, N2/3-alpha] for arbitrary alpha > 0. We prove that in the bulk of the spectrum the local eigenvalue correlation functions and the distribution of the gaps between consecutive eigenvalues coincide with those of the Gaussian orthogonal ensemble.