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.
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DeVille, R.E.L., Vanden-Eijnden, E. A Nontrivial Scaling Limit for Multiscale Markov Chains. J Stat Phys 126, 75–94 (2007). https://doi.org/10.1007/s10955-006-9237-1
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DOI: https://doi.org/10.1007/s10955-006-9237-1