Concentration around a stable equilibrium for the non-autonomous $\Phi_3^4$ model

TL;DR

This paper studies time-dependent singular stochastic PDEs on a 3D torus, demonstrating concentration around a stable equilibrium with Gaussian tail bounds using paracontrolled distributions.

Contribution

It extends the analysis of the  model to non-autonomous cases and establishes concentration results with Gaussian tail bounds.

Findings

Solutions concentrate around a stable equilibrium

Gaussian tail bounds are established for solutions

Extension to non-autonomous  models

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.