Weakly universal dynamical correlations between eigenvalues of large random matrices
Statistical Mechanics
2025-11-11 v1 Disordered Systems and Neural Networks
Mathematical Physics
math.MP
Abstract
It was shown roughly thirty years ago that the density correlations of eigenvalues of large random matrices display a universal form, independent of most of the details of the distribution of the random matrix itself. We show that when the matrix elements evolve according to a Dyson Brownian motion, dynamical correlations retain a large degree of the universality found at equal times when expressed in terms of the characteristics of some partial differential equation in the complex plane.
Keywords
Cite
@article{arxiv.2511.05727,
title = {Weakly universal dynamical correlations between eigenvalues of large random matrices},
author = {Kirone Mallick and Gabriel Téllez and Frédéric van Wijland},
journal= {arXiv preprint arXiv:2511.05727},
year = {2025}
}