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The invariant measure of a one‐dimensional Allen‐Cahn equation with an additive space‐time white noise is studied. This measure is absolutely continuous with respect to a Brownian bridge with a density that can be interpreted as a potential energy term. We consider the sharp interface limit in this setup. In the right scaling this corresponds to a Gibbs‐type measure on a growing interval with decreasing temperature. Our main result is that in the limit we still see exponential convergence towards a curve of minimizers of the energy if the interval does not grow too fast. In the original scaling, the measure is concentrated on configurations with precisely one jump. © 2010 Wiley Periodicals, Inc.

Sharp interface limit for invariant measures of a stochastic Allen‐Cahn equation