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

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  • Chen, Yu-Ting
  • Cox, J. Theodore

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.

Suggested Citation

  • Chen, Yu-Ting & Cox, J. Theodore, 2018. "Weak atomic convergence of finite voter models toward Fleming–Viot processes," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2463-2488.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:7:p:2463-2488
    DOI: 10.1016/j.spa.2017.09.015
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    References listed on IDEAS

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    1. Aldous, David J., 1982. "Markov chains with almost exponential hitting times," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 305-310, September.
    2. Ethier, S. N. & Kurtz, Thomas G., 1994. "Convergence to Fleming-Viot processes in the weak atomic topology," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 1-27, November.
    3. Granovsky, Boris L. & Madras, Neal, 1995. "The noisy voter model," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 23-43, January.
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    Cited by:

    1. Chen, Yu-Ting, 2023. "The replicator equation in stochastic spatial evolutionary games," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 94-139.

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