On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model
Analysis of PDEs
2023-09-26 v3 Mathematical Physics
math.MP
Probability
Abstract
We consider a nonlinear system of ODEs, where the underlying linear dynamics are determined by a Hermitian random matrix ensemble. We prove that the leading order dynamics in the weakly nonlinear, infinite volume limit are determined by a solution to the corresponding kinetic wave equation on a non-trivial timescale. Our proof relies on estimates for Haar-distributed unitary matrices obtained from Weingarten calculus, which may be of independent interest.
Keywords
Cite
@article{arxiv.2203.13748,
title = {On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model},
author = {Guillaume Dubach and Pierre Germain and Benjamin Harrop-Griffiths},
journal= {arXiv preprint arXiv:2203.13748},
year = {2023}
}
Comments
63 pages, 15 figures