The Zealot voter model

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)pk the individual at x consults k ≥ 1 neighbors. If at least one neighbor is 1, they adopt state 1, otherwise they become 0. In addition at rate p0 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.

Duke Scholars

Author Richard Timothy Durrett Mathematics