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title:
Sharp interface limit for invariant measures |
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name:
Weber |
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first name:
Hendrik
|
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location/conference:
SPDE09
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PRESENTATION-link:
http://www.dfg-spp1324.de/download/spde09/material/weber.pdf |
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abstract:
The invariant measure of a 1-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 which 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 limit measure is concentrated on
configurations with precisely one jump. This jump is distributed uniformly. |
