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


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.


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Marek Biskup. "Recent progress on the Random Conductance Model." Probab. Surveys 8 294 - 373, 2011.


Published: 2011
First available in Project Euclid: 30 December 2011

zbMATH: 1245.60098
MathSciNet: MR2861133
Digital Object Identifier: 10.1214/11-PS190

Primary: 60F17 , 60K37
Secondary: 60J45 , 80M40 , 82B43

Keywords: Corrector , effective resistivity , elliptic environment , Heat kernel bounds , Homogenization‎ , quenched invariance principle , Random conductance model

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • 2011
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