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 Probability Surveys > Vol. 8 (2011) open journal systems 

Recent progress on the Random Conductance Model

Marek Biskup

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.

AMS 2000 subject classifications: Primary 60K37, 60F17; secondary 60J45, 82B43, 80M40.

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

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Biskup, Marek, Recent progress on the Random Conductance Model, Probability Surveys, 8, (2011), 294-373 (electronic). DOI: 10.1214/11-PS190.


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