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Matrix Dyson equation and random matrices with correlations

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If you have a question about this talk, please contact Perla Sousi.

We consider large random matrices with general slowly decaying correlation among its entries. We prove universality of local eigenvalue statistics and optimal local law for the resolvent. One key ingredient is a sharp stability analysis of the matrix Dyson equation, the other one is a systematic diagrammatic control of a multivariate cumulant expansion.

This talk is part of the Probability series.

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