Random Matrices with Slow Correlation Decay
arXiv:1705.10661 · doi:10.1017/fms.2019.2
Abstract
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.
arXiv comment41 pages, 1 figure. We corrected a typo in (4.1b)
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