Exponential Ergodicity in Relative Entropy and $L^2$-Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916833787904000 |
|---|---|
| author | Huang, Xing Kopfer, Eva Monmarché, Pierre Ren, Panpan |
| author_facet | Huang, Xing Kopfer, Eva Monmarché, Pierre Ren, Panpan |
| contents | In this paper, we derive exponential ergodicity in relative entropy for general kinetic SDEs under a partially dissipative condition. It covers non-equilibrium situations where the forces are not of gradient type and the invariant measure does not have an explicit density, extending previous results set in the equilibrium case. The key argument is to establish the hypercontractivity of the associated semigroup, which follows from its hyperboundedness and its $L^2$-exponential ergodicity. Moreover, we obtain exponential ergodicity in the $L^2$-Wasserstein distance by combining Talagrand's inequality with a log-Harnack inequality. These results are further extended to the McKean-Vlasov setting and to the associated mean-field interacting particle systems, with convergence rates that are uniform in the number of particles in the latter case, under small nonlinear perturbations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential Ergodicity in Relative Entropy and $L^2$-Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs Huang, Xing Kopfer, Eva Monmarché, Pierre Ren, Panpan Probability In this paper, we derive exponential ergodicity in relative entropy for general kinetic SDEs under a partially dissipative condition. It covers non-equilibrium situations where the forces are not of gradient type and the invariant measure does not have an explicit density, extending previous results set in the equilibrium case. The key argument is to establish the hypercontractivity of the associated semigroup, which follows from its hyperboundedness and its $L^2$-exponential ergodicity. Moreover, we obtain exponential ergodicity in the $L^2$-Wasserstein distance by combining Talagrand's inequality with a log-Harnack inequality. These results are further extended to the McKean-Vlasov setting and to the associated mean-field interacting particle systems, with convergence rates that are uniform in the number of particles in the latter case, under small nonlinear perturbations. |
| title | Exponential Ergodicity in Relative Entropy and $L^2$-Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs |
| topic | Probability |
| url | https://arxiv.org/abs/2507.02518 |