Large deviations and a Kramers' type law for self-stabilizing diffusions
by
Samuel Herrmann
Ecole des Mines de Nancy
Coauthors: Peter Imkeller (Humboldt Universität, Berlin) Dierk Peithmann (Humboldt Universität, Berlin)

We investigate exit times from domains of attraction for the motion of a self-stabilized particle travelling in a geometric (potential type) landscape and perturbed by Brownian noise of small amplitude. Self-stabilization is the effect of including an ensemble-average attraction in addition to the usual state-dependent drift, where the particle is supposed to be suspended in a large population of identical ones. A Kramers' type law for the particle's exit from the potential's domains of attraction and a large deviations principle for the self-stabilizing diffusion will be presented. It turns out that the exit law for the self-stabilizing diffusion coincides with the exit law of a potential diffusion without self-stabilization with a drift component perturbed by average attraction. We will point out that the self-stabilization may substantially delay the exit from domains of attraction, and that the exit location may be completely different. Some examples will be presented.

Date received: June 29, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavj-35.