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October 2019 The zealot voter model
Ran Huo, Rick Durrett
Ann. Appl. Probab. 29(5): 3128-3154 (October 2019). DOI: 10.1214/19-AAP1476


Inspired by the spread of discontent as in the 2016 presidential election, we consider a voter model in which 0’s are ordinary voters and 1’s are zealots. Thinking of a social network, but desiring the simplicity of an infinite object that can have a nontrivial stationary distribution, space is represented by a tree. The dynamics are a variant of the biased voter: if $x$ has degree $d(x)$ then at rate $d(x)p_{k}$ the individual at $x$ consults $k\ge 1$ neighbors. If at least one neighbor is 1, they adopt state 1, otherwise they become 0. In addition at rate $p_{0}$ individuals with opinion 1 change to 0. As in the contact process on trees, we are interested in determining when the zealots survive and when they will survive locally.


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Ran Huo. Rick Durrett. "The zealot voter model." Ann. Appl. Probab. 29 (5) 3128 - 3154, October 2019.


Received: 1 December 2018; Revised: 1 March 2019; Published: October 2019
First available in Project Euclid: 18 October 2019

zbMATH: 07155068
MathSciNet: MR4019884
Digital Object Identifier: 10.1214/19-AAP1476

Primary: 60K35

Keywords: configuarion model , Galton–Watson tree , local survival , randonm graph

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.29 • No. 5 • October 2019
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