Concentration around a stable equilibrium for the non-autonomous $\Phi_3^4$ model
Probability
2025-06-23 v2
Abstract
We consider time-dependent singular stochastic partial differential equations on the three-dimensional torus. These equations are only well-posed after one adds renormalization terms. In order to construct a well-defined notion of solution, one should put the equation in a more general setting. In this article, we consider the paradigm of paracontrolled distributions, and get concentration results around a stable deterministic equilibrium for solutions of non-autonomous generalizations of the model. Specifically, we obtain Gaussian-type tail bounds.
Keywords
Cite
@article{arxiv.2502.21192,
title = {Concentration around a stable equilibrium for the non-autonomous $\Phi_3^4$ model},
author = {Dimitri Faure},
journal= {arXiv preprint arXiv:2502.21192},
year = {2025}
}
Comments
31 pages, v1: Preliminary version 37 pages, v2: Important modifications were made to the structure and I improved the main result