Donnerstag, 09.07.2026: Two-resolvent local laws with decorrelation in energy space
Oleksii Kolupaiev (IST Austria)
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.
| Uhrzeit: |
14:30 |
| Ort: |
C3N14 |
| Gruppe: |
Oberseminar Mathematical Physics |
| Einladender: |
Keppeler, Lemm, Pickl, Teufel, Tumulka |
