Hydrodynamic limit of Exclusion Processes with slow boundaries on hypercubes

Xu, Tiecheng

doi:10.48550/arxiv.2109.14491

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2021

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“…The microscopic models they considered are either defined on a ring with a slow site/slow bond, or defined on a segment with slow boundaries. The results have also been extended to higher dimensions in [7,14].…”

Section: Introductionmentioning

confidence: 90%

The voter model with a slow membrane

Xue,

Zhao

2021

Preprint

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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.

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Section: Introductionmentioning

confidence: 90%