A simple proof of a Kramers’ type law for self-stabilizing diffusions

Abstract

We provide a new proof of a Kramers’ type law for self-stabilizing diffusion. These diffusions correspond to the hydrodynamical limit of a mean-field system of particles and may be seen as the probabilistic interpretation of the granular media equation. We use the same hypotheses as the ones used in the work “Large deviations and a Kramers’ type law for self-stabilizing diffusions” by Herrmann, Imkeller and Peithmann in which the authors obtain a first proof of the statement.