Hydrodynamic Limit for a type of Exclusion Processes with slow bonds in dimension ≥ 2

2010/05/18 by Tertuliano Franco, Franco, Tertuliano, Adriana Neumann +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1005.3079

18 pages, 1 figure

arxiv created 2010/05/18 · openalex publication_date 2010/05/18 · arxiv updated 2010/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Λ be a connected closed region with smooth boundary contained in the d-dimensional continuous torus \bb T^d. In the discrete torus N^-1 \bb T^d_N, we consider a nearest neighbor symmetric exclusion process where occupancies of neighboring sites are exchanged at rates depending on Λ in the following way: if both sites are in Λ or Λ^\complement, the exchange rate is one; If one site is in Λ and the other one is in Λ^\complement and the direction of the bond connecting the sites is e_j, then the exchange rate is defined as N^-1 times the absolute value of the inner product between e_j and the normal exterior vector to \pΛ. We show that this exclusion type process has a non-trivial hydrodynamical behavior under diffusive scaling and, in the continuum limit, particles are not blocked or reflected by ∂Λ. Thus the model represents a system of particles under hard core interaction in the presence of a permeable membrane which slows down the passage of particles between two complementar regions.

Related

• Hydrodynamical behavior of symmetric exclusion with slow bonds
• Hydrodynamic limit for an open facilitated exclusion process with slow and fast boundaries
• Scalings limits for the exclusion process with a slow site
• Superdiffusive Scaling Limits for the Symmetric Exclusion Process with Slow Bonds
• Hydrodynamic behavior of long-range symmetric exclusion with a slow barrier: diffusive regime