Marek Biskup
Published 2011-12-01, updated 2012-01-03Version 3
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.
Comments: 80 pages, version published in Prob. Surveys
Journal: Prob. Surveys 8 (2011) 294-373
Scaling limit for trap models on $\mathbb{Z}^d$
Simple Random Walk on Long Range Percolation Clusters II: Scaling Limits
Local Limit Theorems for the Random Conductance Model and Applications to the Ginzburg-Landau $\nabla\varphi$ Interface Model
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