Concentration around a stable equilibrium for the non-autonomous ${\Phi }_3^4$ model

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 $({\Phi }_3^4)$ model. Specifically, we obtain Gaussian-type tail bounds.

31 pages, v1: Preliminary version 37 pages, v2: Important modifications were made to the structure and I improved the main result