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Sharp interface limit for invariant measures of a stochastic Allen-Cahn equation
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Weber, Hendrik (2010) Sharp interface limit for invariant measures of a stochastic Allen-Cahn equation. Communications on Pure and Applied Mathematics, Vol.63 (No.8). pp. 1071-1109. doi:10.1002/cpa.20323 ISSN 0010-3640.
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Official URL: http://dx.doi.org/10.1002/cpa.20323
Abstract
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. (C) 2010 Wiley Periodicals, Inc.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Communications on Pure and Applied Mathematics | ||||
Publisher: | John Wiley & Sons | ||||
ISSN: | 0010-3640 | ||||
Official Date: | August 2010 | ||||
Dates: |
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Volume: | Vol.63 | ||||
Number: | No.8 | ||||
Number of Pages: | 39 | ||||
Page Range: | pp. 1071-1109 | ||||
DOI: | 10.1002/cpa.20323 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | DFG (Deutsche Forschungsgemeinschaft) | ||||
Grant number: | SFB 611 |
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