English

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 (Φ34)(\Phi_3^4) 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

R2 v1 2026-06-28T22:02:06.228Z