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

Yu Ting Chen; J. Theodore Cox

doi:10.1016/j.spa.2017.09.015

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

Yu Ting Chen, J. Theodore Cox

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 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 language	English (US)
Pages (from-to)	2463-2488
Number of pages	26
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	7
DOIs	https://doi.org/10.1016/j.spa.2017.09.015
State	Published - 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

Access to Document

10.1016/j.spa.2017.09.015

Cite this

@article{05103eea814e4bb79fe86c64c909e99a,

title = "Weak atomic convergence of finite voter models toward Fleming–Viot processes",

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.",

keywords = "Diversity statistics, Empirical measures, Entropy, Fleming–Viot process, Voter model, Weak atomic convergence",

author = "Chen, {Yu Ting} and Cox, {J. Theodore}",

note = "Publisher Copyright: {\textcopyright} 2017",

year = "2018",

month = jul,

doi = "10.1016/j.spa.2017.09.015",

language = "English (US)",

volume = "128",

pages = "2463--2488",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "7",

}

TY - JOUR

T1 - Weak atomic convergence of finite voter models toward Fleming–Viot processes

AU - Chen, Yu Ting

AU - Cox, J. Theodore

PY - 2018/7

Y1 - 2018/7

N2 - 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.

AB - 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.

KW - Diversity statistics

KW - Empirical measures

KW - Entropy

KW - Fleming–Viot process

KW - Voter model

KW - Weak atomic convergence

UR - http://www.scopus.com/inward/record.url?scp=85032213856&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032213856&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2017.09.015

DO - 10.1016/j.spa.2017.09.015

M3 - Article

AN - SCOPUS:85032213856

SN - 0304-4149

VL - 128

SP - 2463

EP - 2488

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 7

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this