Polynomial convergence to equilibrium for a system of interacting particles

Research output: Contribution to journalArticle

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 1 2017

Fingerprint

Convergence to Equilibrium
Particle System
Polynomial
Time Constant
Kinetic energy
Square root
Stochastic Systems
Rate of Convergence
Directly proportional
Energy
Interaction
Polynomials
Model

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Polynomial convergence to equilibrium for a system of interacting particles. / Li, Yao; Young, Lai-Sang.

In: Annals of Applied Probability, Vol. 27, No. 1, 01.02.2017, p. 65-90.

Research output: Contribution to journalArticle

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