Eyring-Kramers formula for the mean exit time of non-Gibbsian elliptic processes: the non characteristic boundary case
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915506615746560 |
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| author | Peutrec, Dorian Le Michel, Laurent Nectoux, Boris |
| author_facet | Peutrec, Dorian Le Michel, Laurent Nectoux, Boris |
| contents | In this work, we derive a new sharp asymptotic equivalent in the small temperature regime $h\to 0$ for the mean exit time from a bounded domain for the non-reversible process $dX\_t=b(X\_t)dt + \sqrt h \, dB\_t$ under a generic orthogonal decomposition of $b$ and when the boundary of $Ω$ is assumed to be \textit{non characteristic}. The main contribution of this work lies in the fact that we do not assume that the process $(X\_t,t\ge 0)$ is \textit{Gibbsian}. In this case, a new correction term characterizing the \textit{non-Gibbsianness} of the process appears in the equivalent of the mean exit time. The proof is mainly based on tools from spectral and semi-classical analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_17678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eyring-Kramers formula for the mean exit time of non-Gibbsian elliptic processes: the non characteristic boundary case Peutrec, Dorian Le Michel, Laurent Nectoux, Boris Analysis of PDEs Mathematical Physics Probability Spectral Theory In this work, we derive a new sharp asymptotic equivalent in the small temperature regime $h\to 0$ for the mean exit time from a bounded domain for the non-reversible process $dX\_t=b(X\_t)dt + \sqrt h \, dB\_t$ under a generic orthogonal decomposition of $b$ and when the boundary of $Ω$ is assumed to be \textit{non characteristic}. The main contribution of this work lies in the fact that we do not assume that the process $(X\_t,t\ge 0)$ is \textit{Gibbsian}. In this case, a new correction term characterizing the \textit{non-Gibbsianness} of the process appears in the equivalent of the mean exit time. The proof is mainly based on tools from spectral and semi-classical analysis. |
| title | Eyring-Kramers formula for the mean exit time of non-Gibbsian elliptic processes: the non characteristic boundary case |
| topic | Analysis of PDEs Mathematical Physics Probability Spectral Theory |
| url | https://arxiv.org/abs/2509.17678 |