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<p>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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((\Phi _3^4)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msubsup> <mi mathvariant="normal">Φ</mi> <mn>3</mn> <mn>4</mn> </msubsup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> model. Specifically, we obtain Gaussian-type tail bounds.</p>

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Concentration around a stable equilibrium for the non-autonomous \(\Phi _3^4\) model

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Dimitri Faure

摘要

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 \((\Phi _3^4)\) ( Φ 3 4 ) model. Specifically, we obtain Gaussian-type tail bounds.