Concentration around a stable equilibrium for the non-autonomous $Φ_3^4$ model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909653467660288 |
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| author | Faure, Dimitri |
| author_facet | Faure, Dimitri |
| contents | 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 $(Φ_3^4)$ model. Specifically, we obtain Gaussian-type tail bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concentration around a stable equilibrium for the non-autonomous $Φ_3^4$ model Faure, Dimitri Probability 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 $(Φ_3^4)$ model. Specifically, we obtain Gaussian-type tail bounds. |
| title | Concentration around a stable equilibrium for the non-autonomous $Φ_3^4$ model |
| topic | Probability |
| url | https://arxiv.org/abs/2502.21192 |