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arXiv · 2203.13748

On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model

Guillaume Dubach·Pierre Germain·Benjamin Harrop-Griffiths
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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.

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Guillaume Dubach, Pierre Germain, Benjamin Harrop-Griffiths. 2022-03-25. On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model. https://arxiv.org/abs/2203.13748

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