## Journal of Applied Probability

### Hydrodynamic limit for a type of exclusion process with slow bonds in dimension d ≥ 2

#### Abstract

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.

#### Article information

Source
J. Appl. Probab., Volume 48, Number 2 (2011), 333-351.

Dates
First available in Project Euclid: 21 June 2011

https://projecteuclid.org/euclid.jap/1308662631

Digital Object Identifier
doi:10.1239/jap/1308662631

Mathematical Reviews number (MathSciNet)
MR2840303

Zentralblatt MATH identifier
1220.82076

#### Citation

Franco, Tertuliano; Neumann, Adriana; Valle, Glauco. Hydrodynamic limit for a type of exclusion process with slow bonds in dimension d ≥ 2. J. Appl. Probab. 48 (2011), no. 2, 333--351. doi:10.1239/jap/1308662631. https://projecteuclid.org/euclid.jap/1308662631

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