A nontrivial scaling limit for multiscale Markov chains

R. E Lee Deville, Eric Vanden Eijnden

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)75-94
Number of pages20
JournalJournal of Statistical Physics
Volume126
Issue number1
DOIs
StatePublished - Jan 2007

Fingerprint

Markov chains
Scaling Limit
Markov chain
Time Scales
gait
scaling
Molecular Motor
Rare Events
Stochastic Resonance
Mean-field Approximation
Gait
regularity
Regularity
approximation
Experiment
Model
Standards

Keywords

  • Large deviations
  • Markov chain
  • Molecular motors
  • Scaling limit
  • Self-induced stochastic resonance

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

A nontrivial scaling limit for multiscale Markov chains. / Deville, R. E Lee; Vanden Eijnden, Eric.

In: Journal of Statistical Physics, Vol. 126, No. 1, 01.2007, p. 75-94.

Research output: Contribution to journalArticle

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