Two-resolvent local laws with decorrelation in energy space.
Date: 1. July 2026Time: 16:30 – 18:00
Title: Two-resolvent local laws with decorrelation in energy space.
Abstract: Let $G_1(w_1), G_2(w_2)$ be resolvents of two large random matrices. For a broad class of mean field models it is known that $G_1(w_1)G_2(w_2)$ concentrates around a deterministic matrix, with fluctuations controlled from above by $eta:=min{|Im w_1|,|Im w_2|}$. Such estimates are known as two-resolvent local laws. In this talk, I will discuss both Hermitian and non-Hermitian random matrix ensembles. For each setting, I will present an improved two-resolvent local law whose control parameter captures the dependence on $w_1-w_2$ and other model parameters in an optimal way. I will then discuss several applications of these results, focusing on the recent proof of hyperuniformity for the eigenvalue process of a non-Hermitian matrix with independent identically distributed entries. The talk is based on several recent joint works with G. Cipolloni, L. Erd{H o}s, J. Henheik and Z. Bao.