Probability Surveys

Recent progress on the Random Conductance Model

Marek Biskup

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Abstract

Recent progress on the understanding of the Random Conductance Model is reviewed and commented. A particular emphasis is on the results on the scaling limit of the random walk among random conductances for almost every realization of the environment, observations on the behavior of the effective resistance as well as the scaling limit of certain models of gradient fields with non-convex interactions. The text is an expanded version of the lecture notes for a course delivered at the 2011 Cornell Summer School on Probability.

Article information

Source
Probab. Surveys, Volume 8 (2011), 294-373.

Dates
First available in Project Euclid: 30 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.ps/1325264815

Digital Object Identifier
doi:10.1214/11-PS190

Mathematical Reviews number (MathSciNet)
MR2861133

Zentralblatt MATH identifier
1245.60098

Subjects
Primary: 60K37: Processes in random environments 60F17: Functional limit theorems; invariance principles
Secondary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 82B43: Percolation [See also 60K35] 80M40: Homogenization

Keywords
Random conductance model elliptic environment quenched invariance principle corrector heat kernel bounds effective resistivity homogenization

Citation

Biskup, Marek. Recent progress on the Random Conductance Model. Probab. Surveys 8 (2011), 294--373. doi:10.1214/11-PS190. https://projecteuclid.org/euclid.ps/1325264815


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