The voter model with a slow membrane

2021/11/21 by Xue, Xiaofeng, Zhao, Linjie · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.10821

Abstract

We introduce the voter model on the infinite lattice with a slow membrane and investigate its hydrodynamic behavior and nonequilibrium fluctuations. The model is defined as follows: a voter adopts one of its neighbors' opinion at rate one except for neighbors crossing the hyperplane \x:x₁ = 1/2\, where the rate is αN^-β. Above, α>0, β≥ 0 are two parameters and N is the scaling parameter. The hydrodynamic equation turns out to be heat equation with various boundary conditions depending on the value of β. For the nonequilibrium fluctuations, the limit is described by generalized Ornstein-Uhlenbeck process with certain boundary condition corresponding to the hydrodynamic equation.

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