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arXiv · 1705.10661

Random Matrices with Slow Correlation Decay

László Erdős·Torben Krüger·Dominik Schröder
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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.

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László Erdős, Torben Krüger, Dominik Schröder. 2017-05-30. Random Matrices with Slow Correlation Decay. https://doi.org/10.1017/fms.2019.2

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