Recurrence and ergodicity of interacting particle systems

J. Theodore Cox, Achim Klenke

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

Many interacting particle systems with short range interactions are not ergodic, but converge weakly towards a mixture of their ergodic invariant measures. The question arises whether a.s. the process eventually stays close to one of these ergodic states, or if it changes between the attainable ergodic states infinitely often ("recurrence"). Under the assumption that there exists a convergence-determining class of distributions that is (strongly) preserved under the dynamics, we show that the system is in fact recurrent in the above sense. We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we answer a question raised by Ed Perkins concerning the change of the locally predominant type in a model of mutually catalytic branching.

Original languageEnglish (US)
Pages (from-to)239-255
Number of pages17
JournalProbability Theory and Related Fields
Volume116
Issue number2
DOIs
StatePublished - Feb 2000

Keywords

  • Clustering
  • Ergodicity
  • Interacting particle systems
  • Longtime behavior
  • Mutually catalytic branching
  • Recurrence

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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