Abstract: We consider the sharp interface limit for the 1D stochastic Allen-Cahn equation, and extend earlier work by Funaki to the full small noise regime. The main new idea is the construction of a series of functional correctors, which are designed to recursively cancel potential divergences. In addition, in order to show these correctors are well-behaved, we develop a systematic decomposition of functional derivatives of the deterministic Allen-Cahn flow of all orders. This talk is based on joint work with Weijun Xu (BICMR) and Wenhao Zhao (EPFL).
