Concentration around a stable equilibrium for the non-autonomous Φ₃⁴ model

2025/02/28 by Faure, Dimitri
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.21192

openalex publication_date 2025/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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) model. Specifically, we obtain Gaussian-type tail bounds.

Related

• Paracontrolled Distributions and the 3-dimensional Stochastic Quantization Equation
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• Lattice approximation to the dynamical Φ₃⁴ model