The voter model with a slow membrane

Xiaofeng Xue (1) , Linjie Zhao (2)

1 BJTU - Beijing Jiaotong University
2 Paradyse - Systèmes de particules et systèmes dynamiques

We introduce the voter model on the infinite lattice with a slow membrane and investigate its hydrodynamic behavior. The model is defined as follows: a voter adopts one of its neighbors' opinion at rate one except for neighbors crossing the hyperplane {x : x 1 = 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. The proof is based on duality method.

Mots clés: Voter model; heat equation; boundary conditions; duality

Domaines: Probabilités [math.PR]

Xiaofeng Xue, Linjie Zhao. The voter model with a slow membrane. 2022. ⟨hal-03619411⟩