Universality of random matrix dynamics
Mathematical Physics
2023-07-19 v1 Soft Condensed Matter
math.MP
Abstract
We discuss the concept of width-to-spacing ratio which plays the central role in the description of local spectral statistics of evolution operators in multiplicative and additive stochastic processes for random matrices. We show that the local spectral properties are highly universal and depend on a single parameter being the width-to-spacing ratio. We discuss duality between the kernel for Dysonian Brownian motion and the kernel for the Lyapunov matrix for the product of Ginibre matrices.
Keywords
Cite
@article{arxiv.2005.09286,
title = {Universality of random matrix dynamics},
author = {Zdzislaw Burda},
journal= {arXiv preprint arXiv:2005.09286},
year = {2023}
}
Comments
15 pages, 3 figures