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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2509.13806 |
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| _version_ | 1866916954436009984 |
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| author | Laarne, Petri |
| author_facet | Laarne, Petri |
| contents | We study the dynamics of a stochastic heat equation with $γ\sin(βu)$ nonlinearity on one-dimensional torus. We show an Eyring--Kramers law for the jump rate between potential wells in the small-noise limit, and that the transition state undergoes a bifurcation at $γβ= 1$. The argument follows the potential-theoretic approach of Berglund and Gentz [Electron. J. Probab. 2013]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metastable transition times of the 1D dynamical sine-Gordon model Laarne, Petri Mathematical Physics Probability 60H15 (Primary), 60J45, 60J60, 81S20, 82C44 (Secondary) We study the dynamics of a stochastic heat equation with $γ\sin(βu)$ nonlinearity on one-dimensional torus. We show an Eyring--Kramers law for the jump rate between potential wells in the small-noise limit, and that the transition state undergoes a bifurcation at $γβ= 1$. The argument follows the potential-theoretic approach of Berglund and Gentz [Electron. J. Probab. 2013]. |
| title | Metastable transition times of the 1D dynamical sine-Gordon model |
| topic | Mathematical Physics Probability 60H15 (Primary), 60J45, 60J60, 81S20, 82C44 (Secondary) |
| url | https://arxiv.org/abs/2509.13806 |