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Recent progress on the random conductance model. (English) Zbl 1245.60098
Summary: 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.

MSC:
60K37 Processes in random environments
60F17 Functional limit theorems; invariance principles
60J45 Probabilistic potential theory
82B43 Percolation
80M40 Homogenization for problems in thermodynamics and heat transfer
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