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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.13099 |
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| _version_ | 1866908940226265088 |
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| author | Guillin, Arnaud Lu, D I Nectoux, Boris Wu, Liming |
| author_facet | Guillin, Arnaud Lu, D I Nectoux, Boris Wu, Liming |
| contents | In this work, we investigate the compactness and the long time behavior of killed Feynman-Kac semigroups of various processes arising from statistical physics with very general singular Schr{ö}dinger potentials. The processes we consider cover a large class of processes used in statistical physics, with strong links with quantum mechanics and (local or not) Schr{ö}dinger operators (including e.g. fractional Laplacians). For instance we consider solutions to elliptic differential equations, L{é}vy processes, the kinetic Langevin process with locally Lipschitz gradient fields, and systems of interacting L{é}vy particles. Our analysis relies on a Perron-Frobenius type theorem derived in a previous work [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.] for Feller kernels and on the tools introduced in [L. Wu, 2004, Probab. Theory Relat. Fields] to compute bounds on the essential spectral radius of a bounded nonnegative kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long time behavior of killed Feynman-Kac semigroups with singular Schr{ö}dinger potentials Guillin, Arnaud Lu, D I Nectoux, Boris Wu, Liming Probability In this work, we investigate the compactness and the long time behavior of killed Feynman-Kac semigroups of various processes arising from statistical physics with very general singular Schr{ö}dinger potentials. The processes we consider cover a large class of processes used in statistical physics, with strong links with quantum mechanics and (local or not) Schr{ö}dinger operators (including e.g. fractional Laplacians). For instance we consider solutions to elliptic differential equations, L{é}vy processes, the kinetic Langevin process with locally Lipschitz gradient fields, and systems of interacting L{é}vy particles. Our analysis relies on a Perron-Frobenius type theorem derived in a previous work [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.] for Feller kernels and on the tools introduced in [L. Wu, 2004, Probab. Theory Relat. Fields] to compute bounds on the essential spectral radius of a bounded nonnegative kernel. |
| title | Long time behavior of killed Feynman-Kac semigroups with singular Schr{ö}dinger potentials |
| topic | Probability |
| url | https://arxiv.org/abs/2411.13099 |