- Probab. Surveys
- Volume 8 (2011), 294-373.
Recent progress on the Random Conductance Model
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.
Probab. Surveys, Volume 8 (2011), 294-373.
First available in Project Euclid: 30 December 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K37: Processes in random environments 60F17: Functional limit theorems; invariance principles
Secondary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 82B43: Percolation [See also 60K35] 80M40: Homogenization
Biskup, Marek. Recent progress on the Random Conductance Model. Probab. Surveys 8 (2011), 294--373. doi:10.1214/11-PS190. https://projecteuclid.org/euclid.ps/1325264815