Diffusive fluctuations of long-range symmetric exclusion with a slow barrier

2022/12/23 by Pedro Cardoso, Cardoso, Pedro, Patrícia GonÇAlves +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2212.12089

openalex publication_date 2022/12/23 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

Abstract

In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in ℤ with long jumps. The transition probability of the jump from x to y is proportional to |x-y|^-γ-1. Here we restrict to the choice γ≥ 2 so that the system has a diffusive behavior. Moreover, when particles move between ℤ_-^* and \mathbb N, the jump rates are slowed down by a factor αn^-β, where α>0, β≥ 0 and n is the scaling parameter. Depending on the values of β and γ, we obtain several stochastic partial differential equations, corresponding to a heat equation without boundary conditions, or with Robin boundary conditions or Neumann boundary conditions.

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