Occupation time large deviations of the voter model

Maury Bramson, J. Theodore Cox, David Griffeath

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

This paper is a sequel to [5] and [6]. We continue our study of occupation time large deviation probabilities for some simple infinite particle systems by analysing the so-called voter model ζt (see e.g., [11] or [8]). In keeping with our previous results, we show that the large deviations are "classical" in high dimensions (d≧5 for ζt) but "fat" in low dimensions (d≦4). Interaction distinguishes the voter model from the independent particle systems of [5] and [6], and consequently exact computations no longer seem feasible. Instead, we derive upper and lower bounds which capture the asymptotic decay rate of the large deviation tails.

Original languageEnglish (US)
Pages (from-to)401-413
Number of pages13
JournalProbability Theory and Related Fields
Volume77
Issue number3
DOIs
StatePublished - Mar 1988

ASJC Scopus subject areas

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

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