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

Dimitri Faure

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arXiv · 2502.21192

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

Dimitri Faure

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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.

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Dimitri Faure. 2025-02-28. Concentration around a stable equilibrium for the non-autonomous $\Phi_3^4$ model. https://arxiv.org/abs/2502.21192

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