L2 geometric ergodicity for the kinetic Langevin process with non-equilibrium steady states
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929692195422208 |
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| author | Monmarché, Pierre |
| author_facet | Monmarché, Pierre |
| contents | In non-equilibrium statistical physics models, the invariant measure $μ$ of the process does not have an explicit density. In particular the adjoint $L^*$ in $L^2(μ)$ of the generator $L$ is unknown and many classical techniques fail in this situation. An important progress has been made in [5] where functional inequalities are obtained for non-explicit steady states of kinetic equations under rather general conditions. However in [5] in the kinetic case the geometric ergodicity is only deduced from the functional inequalities for the case with conservative forces, corresponding to explicit steady states. In this note we obtain $L^2$ convergence rates in the non-equilibrium case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_18004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | L2 geometric ergodicity for the kinetic Langevin process with non-equilibrium steady states Monmarché, Pierre Analysis of PDEs Mathematical Physics Probability In non-equilibrium statistical physics models, the invariant measure $μ$ of the process does not have an explicit density. In particular the adjoint $L^*$ in $L^2(μ)$ of the generator $L$ is unknown and many classical techniques fail in this situation. An important progress has been made in [5] where functional inequalities are obtained for non-explicit steady states of kinetic equations under rather general conditions. However in [5] in the kinetic case the geometric ergodicity is only deduced from the functional inequalities for the case with conservative forces, corresponding to explicit steady states. In this note we obtain $L^2$ convergence rates in the non-equilibrium case. |
| title | L2 geometric ergodicity for the kinetic Langevin process with non-equilibrium steady states |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2501.18004 |