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Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2019

Metastability of one-dimensional, non-reversible diffusions with periodic boundary conditions

Claudio Landim
I. Seo

Résumé

We consider small perturbations of a dynamical system on the one-dimensional torus. We derive sharp estimates for the pre-factor of the stationary state, we examine the asymptotic behavior of the solutions of the Hamilton-Jacobi equation for the pre-factor, we compute the capacities between disjoint sets, and we prove the metastable behavior of the process among the deepest wells following the martingale approach. We also present a bound for the probability that a Markov process hits a set before some fixed time in terms of the capacity of an enlarged process.

Dates et versions

hal-01728588 , version 1 (11-03-2018)

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Claudio Landim, I. Seo. Metastability of one-dimensional, non-reversible diffusions with periodic boundary conditions. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2019, ⟨10.1214/18-AIHP936⟩. ⟨hal-01728588⟩
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