Eyring-Kramers Law for the Underdamped Langevin Process
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908826279608320 |
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| author | Lee, Seungwoo Ramil, Mouad Seo, Insuk |
| author_facet | Lee, Seungwoo Ramil, Mouad Seo, Insuk |
| contents | Consider the underdamped Langevin process $(q(t),p(t))_{t\geq0}$ in $\R^d\times\R^d$. We derive the low-temperature asymptotic of its mean-transition time between basins of attraction for a double-well potential. This asymptotic is called Eyring-Kramers law and often relies in the literature on Potential theory tools which are ill-defined for hypoelliptic processes like the underdamped Langevin process. In this work, we implement a novel approach which circumvents the use of these traditional methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eyring-Kramers Law for the Underdamped Langevin Process Lee, Seungwoo Ramil, Mouad Seo, Insuk Probability Consider the underdamped Langevin process $(q(t),p(t))_{t\geq0}$ in $\R^d\times\R^d$. We derive the low-temperature asymptotic of its mean-transition time between basins of attraction for a double-well potential. This asymptotic is called Eyring-Kramers law and often relies in the literature on Potential theory tools which are ill-defined for hypoelliptic processes like the underdamped Langevin process. In this work, we implement a novel approach which circumvents the use of these traditional methods. |
| title | Eyring-Kramers Law for the Underdamped Langevin Process |
| topic | Probability |
| url | https://arxiv.org/abs/2503.12610 |