Invariant Gibbs measure for Anderson nonlinear wave equation
Probability
2025-04-09 v3 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We study the Gaussian measure whose covariance is related to the Anderson Hamiltonian operator, proving that it admits a regular coupling to the (standard) Gaussian free field exploiting the stochastic optimal control formulation of Gibbs measures. Using this coupling, we define the renormalized powers of the Anderson free field and we prove that the associated quartic Gibbs measure is invariant under the flow of a nonlinear wave equation with renormalized cubic nonlinearity.
Keywords
Cite
@article{arxiv.2309.01635,
title = {Invariant Gibbs measure for Anderson nonlinear wave equation},
author = {Nikolay Barashkov and Francesco C. De Vecchi and Immanuel Zachhuber},
journal= {arXiv preprint arXiv:2309.01635},
year = {2025}
}
Comments
We have corrected some typos and updated the title. This version has been accepted for publication in "Annali della Scuola Normale Superiore di Pisa - Classe di Scienze"