A Nontrivial Scaling Limit for Multiscale Markov Chains

Author: DeVille R.   Vanden-Eijnden Eric  

Publisher: Springer Publishing Company

ISSN: 0022-4715

Source: Journal of Statistical Physics, Vol.126, Iss.1, 2007-01, pp. : 75-94

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Abstract

We consider Markov chains with fast and slow variables and show that in a suitable scaling limit, the dynamics becomes deterministic, yet is far away from the standard mean field approximation. This new limit is an instance of self-induced stochastic resonance which arises due to matching between a rare event timescale on the one hand and the natural timescale separation in the underlying problem on the other. Here it is illustrated on a model of a molecular motor, where it is shown to explain the regularity of the motor gait observed in some experiments.