Journal
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
Volume 51, Issue 1, Pages 129-166Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/13-AIHP575
Keywords
Metastability; Metastable transition time; Parabolic stochastic partial differential equations; Reaction-diffusion equations; Stochastic Allen-Cahn equations; Eyring-Kramers formula
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Funding
- ANR MANEGE
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We consider a class of parabolic semi-linear stochastic partial differential equations driven by space-time white noise on a compact space interval. Our aim is to obtain precise asymptotics of the transition times between metastable states. A version of the so-called Eyring-Kramers formula is proven in an infinite dimensional setting. The proof is based on a spatial finite difference discretization of the stochastic partial differential equation. The expected transition time is computed for the finite dimensional approximation and controlled uniformly in the dimension.
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