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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2005.12581 |
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| _version_ | 1866917710667972608 |
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| author | Dagallier, B. |
| author_facet | Dagallier, B. |
| contents | We study large deviations for a Markov process on curves in $\mathbb{Z}^2$ mimicking the motion of an interface. Our dynamics can be tuned with a parameter $β$, which plays the role of an inverse temperature, and coincides at $β$ = $\infty$ with the zero-temperature Ising model with Glauber dynamics, where curves correspond to the boundaries of droplets of one phase immersed in a sea of the other one. We prove that contours typically follow a motion by curvature with an influence of the parameter $β$, and establish large deviations bounds at all large enough $β$ < $\infty$. The diffusion coefficient and mobility of the model are identified and correspond to those predicted in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_12581 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Motion by curvature and large deviations for an interface dynamics on $\mathbb{Z}^2$ Dagallier, B. Mathematical Physics Probability We study large deviations for a Markov process on curves in $\mathbb{Z}^2$ mimicking the motion of an interface. Our dynamics can be tuned with a parameter $β$, which plays the role of an inverse temperature, and coincides at $β$ = $\infty$ with the zero-temperature Ising model with Glauber dynamics, where curves correspond to the boundaries of droplets of one phase immersed in a sea of the other one. We prove that contours typically follow a motion by curvature with an influence of the parameter $β$, and establish large deviations bounds at all large enough $β$ < $\infty$. The diffusion coefficient and mobility of the model are identified and correspond to those predicted in the literature. |
| title | Motion by curvature and large deviations for an interface dynamics on $\mathbb{Z}^2$ |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2005.12581 |