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Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit


 
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1. Title Title of document Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit
 
2. Creator Author's name, affiliation, country Alessandra Faggionato; Department of Mathematics. University La Sapienza, Rome. Italy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) disordered system; bond percolation; random walk in random environment; exclusion process; homogenization
 
3. Subject Subject classification 60K35; 60J27; 82C44
 
4. Description Abstract We consider a stationary and ergodic random field $\{\omega (b):b \in \mathbb{E}_d \}$ parameterized by the family of bonds in $\mathbb{Z}^d$, $d\geq 2$. The random variable $\omega(b)$ is thought of as the conductance of bond $b$ and it ranges in a finite interval $[0,c_0]$. Assuming that the set of bonds with positive conductance has a unique infinite cluster $\mathcal{C}(\omega)$, we prove homogenization results for the random walk among random conductances on $\mathcal{C}(\omega)$. As a byproduct, applying the general criterion of Faggionato (2007) leading to the hydrodynamic limit of exclusion processes with bond--dependent transition rates, for almost all realizations of the environment we prove the hydrodynamic limit of simple exclusion processes among random conductances on $\mathcal{C}(\omega)$. The hydrodynamic equation is given by a heat equation whose diffusion matrix does not depend on the environment. We do not require any ellipticity condition. As special case, $\mathcal{C}(\omega)$ can be the infinite cluster of supercritical Bernoulli bond percolation.
 
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7. Date (YYYY-MM-DD) 2008-12-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/591
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-591
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
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