On the convergence of densities of finite voter models to the Wright-Fisher diffusion

Yu Ting Chen, Jihyeok Choi, J. Theodore Cox

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We study voter models defined on large finite sets. Through a perspective emphasizing the martingale property of voter density processes, we prove that in general, their convergence to the Wright-Fisher diffusion only involves certain averages of the voter models over a small number of spatial locations. This enables us to identify suitable mixing conditions on the underlying voting kernels, one of which may just depend on their eigenvalues in some contexts, to obtain the convergence of density processes. We show by examples that these conditions are satisfied by a large class of voter models on growing finite graphs.

Original languageEnglish (US)
Pages (from-to)286-322
Number of pages37
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume52
Issue number1
DOIs
StatePublished - Feb 2016

Keywords

  • Dual processes
  • Interacting particle system
  • Semimartingale convergence theorem
  • Voter model
  • Wright-Fisher diffusion

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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