Polynomial convergence to equilibrium for a system of interacting particles

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Abstract

We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent with analogous mechanical models. Our main result is that the rate of convergence to equilibrium for such a system is ∼t-2, more precisely it is faster than a constant times t-2+ε for any ε > 0. A discussion of exponential vs. polynomial convergence for similar particle systems is included.

Original languageEnglish (US)
Pages (from-to)65-90
Number of pages26
JournalAnnals of Applied Probability
Volume27
Issue number1
DOIs
StatePublished - Feb 2017

Keywords

  • Interacting particle model
  • Markov jump process
  • Polynomial convergence rate

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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