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 |
Keywords:
random conductance model; elliptic environment; quenched invariance principle; corrector; heat kernel bounds; effective resistivity; homogenizationReferences:
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