Weak atomic convergence of finite voter models toward Fleming–Viot processes

Yu Ting Chen, J. Theodore Cox

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider the empirical measures of multi-type voter models with mutation on large finite sets, and prove their weak atomic convergence in the sense of Ethier and Kurtz (1994) toward a Fleming–Viot process. Convergence in the weak atomic topology is strong enough to answer a line of inquiry raised by Aldous (2013) concerning the distributions of the corresponding entropy processes and diversity processes for types.

Original languageEnglish (US)
Pages (from-to)2463-2488
Number of pages26
JournalStochastic Processes and their Applications
Volume128
Issue number7
DOIs
StatePublished - Jul 2018

Keywords

  • Diversity statistics
  • Empirical measures
  • Entropy
  • Fleming–Viot process
  • Voter model
  • Weak atomic convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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