Matrix Dyson equation and random matrices with correlations

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.

• Speaker: Laszlo Erdös (IST Austria)
• Tuesday 31 October 2017, 16:15–17:15
• Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
• Series: Probability; organiser: Perla Sousi.