تقرير
An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two
| العنوان: | An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two |
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| المؤلفون: | Berglund, Nils, Di Gesù, Giacomo, Weber, Hendrik |
| المصدر: | Electron. J. Probab. 22 (2017), no. 41, 27 pp |
| سنة النشر: | 2016 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematical Physics, 60H15, 35K57 (primary), 81S20, 82C28 (secondary) |
| الوصف: | We study spectral Galerkin approximations of an Allen--Cahn equation over the two-dimensional torus perturbed by weak space-time white noise of strength $\sqrt{\varepsilon}$. We introduce a Wick renormalisation of the equation in order to have a system that is well-defined as the regularisation is removed. We show sharp upper and lower bounds on the transition times from a neighbourhood of the stable configuration $-1$ to the stable configuration $1$ in the asymptotic regime $\varepsilon \to 0$. These estimates are uniform in the discretisation parameter $N$, suggesting an Eyring-Kramers formula for the limiting renormalised stochastic PDE. The effect of the "infinite renormalisation" is to modify the prefactor and to replace the ratio of determinants in the finite-dimensional Eyring-Kramers law by a renormalised Carleman-Fredholm determinant. Comment: 28 pages, 1 Figure. Revised version with expanded discussion |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1214/17-EJP60 |
| URL الوصول: | http://arxiv.org/abs/1604.05742 |
| رقم الأكسشن: | edsarx.1604.05742 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1214/17-EJP60 |
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