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.
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