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June 2011 Hydrodynamic limit for a type of exclusion process with slow bonds in dimension d ≥ 2
Tertuliano Franco, Adriana Neumann, Glauco Valle
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J. Appl. Probab. 48(2): 333-351 (June 2011). DOI: 10.1239/jap/1308662631


Let Λ be a connected closed region with smooth boundary contained in the d-dimensional continuous torus Td. In the discrete torus N-1TdN, 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 Λc, the exchange rate is 1; if one site is in Λ and the other site is in Λc, and the direction of the bond connecting the sites is ej, then the exchange rate is defined as N-1 times the absolute value of the inner product between ej and the normal exterior vector to ∂Λ. We show that this exclusion-type process has a nontrivial 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 complementary regions.


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Tertuliano Franco. Adriana Neumann. Glauco Valle. "Hydrodynamic limit for a type of exclusion process with slow bonds in dimension d ≥ 2." J. Appl. Probab. 48 (2) 333 - 351, June 2011.


Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1220.82076
MathSciNet: MR2840303
Digital Object Identifier: 10.1239/jap/1308662631

Primary: 80C22
Secondary: 60-XX

Keywords: Exclusion process , Hydrodynamic limit , nonhomogeneous media

Rights: Copyright © 2011 Applied Probability Trust


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Vol.48 • No. 2 • June 2011
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