On the short time asymptotic of the stochastic Allen-Cahn equation
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🧮 math.PR
math.AP
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allen-cahnequationresultshortsolutionsstochastictimeaccording
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A description of the short time behavior of solutions of the Allen-Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional stochastic forcing. This extends a similar result of Funaki in spatial dimension $n=2$ to arbitrary dimensions.
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