多维随机Allen-Cahn方程的不变测度的低噪声极限
Low noise limit for the invariant measure of a multi-dimensional stochastic Allen-Cahn equation
摘要：
研究了d+1维离散随机Allen-Cahn方程在低噪声极限下的不变测度.我们考虑一个长方体区域，并在两个相对的面上施加两个稳定相作为边界条件。然后，我们采取一个联合限制的温度和网格的离散化去为零，而域的大小的增长。我们的主要结果是，不变测度集中指数快速周围的自由能泛函的最小值，如果域不增长太快。
英文摘要：
We study the invariant measure of a discretized stochastic Allen-Cahn equation in d+1 dimensions in the low noise limit. We consider a cuboidal domain and impose the two stable phases as boundary conditions at two opposite faces. We then take a joint limit where the temperature and the mesh of the discretization go to zero while the size of the domain grows. Our main result is that the invariant measures concentrate exponentially fast around the minimizers of the free energy functional if the domain does not grow too fast.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
