Non-Gaussian fluctuations and decorrelations in random matrix theory (Oleksii Kolupaiev, ISTA, Vienna)

14.09.2026 16:15 – 18:00

Let W = W* be a large random matrix. For a broad range of ensembles it is known that the resolvent G(z) := (W −z)^{−1} concentrates around a deterministic quantity as long as |ℑz| is larger than the local eigenvalue spacing of W. This is the so-called single-resolvent local law. Multi-resolvent local laws extend this framework by showing that products of several resolvents also concentrate. In this talk, I will discuss two phenomena that provide additional information beyond the standard local laws: decorrelation in energy space and gains from taking expectations. I will also present several recent applications of these results, which would not be accessible via standard local laws. These applications include non-Gaussian corrections to fluctuations in local laws, law of fractional logarithm for Wigner minor process and hyperuniformity of eigenvalues of non-Hermitian random matrices. The talk is based on several recent joint works with Z. Bao, G. Cipolloni, L. Erdos and J. Henheik.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Math Physics"

entrée libre