Triviality of the 2D stochastic Allen-Cahn equation

Martin Hairer (University of Warwick)
Marc Daniel Ryser (Duke University)
Hendrik Weber (University of Warwick)

Abstract


We consider the stochastic Allen-Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to 0, independently of the initial condition. If the intensity of the noise simultaneously converges to 0 at a sufficiently fast rate, then the solutions converge to those of the deterministic equation. At the critical rate, the limiting solution is still deterministic, but it exhibits an additional damping term.

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Pages: 1-14

Publication Date: May 30, 2012

DOI: 10.1214/EJP.v17-1731

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