2017/05/31 by László Erdős, Torben Krüger, Dominik Schröder
Mathematics · Physics and Astronomy · #math-ph #math.MP #math.PR #msc:15B52 #msc:60B20
paper · pdf · doi:10.1017/fms.2019.2
published as Forum Math. Sigma 7 (2019), e8, 89 pp · 41 pages, 1 figure. We corrected a typo in (4.1b)
arxiv created 2020/05/29 · arxiv updated 2020/06/01
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of [arXiv:1604.08188] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.