Bulk universality for generalized Wigner matrices

• 成果类型: Article
• 署名作者: Erdos, Laszlo; Yau, Horng-Tzer; Yin, Jun
• 署名单位: Harvard University; University of Munich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0390-3
• 发表日期: 2012
• 页码: 341-407
• 关键词: orthogonal polynomials; asymptotics; eigenvalues; Respect; density

摘要

Consider N x N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure nu (ij) with a subexponential decay. Let be the variance for the probability measure nu (ij) with the normalization property that for all j. Under essentially the only condition that for some constant c > 0, we prove that, in the limit N -> a, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). We also show that for band matrices with bandwidth M the local semicircle law holds to the energy scale M (-1).