| 概要 | A random resistor network is a finite or infinite graph where edges are assigned non-negative weights called resistances (or, taking reciprocals, conductances); one then typically studies the solutions to the Kirchhoff and Ohm laws with given boundary data. These networks are of interest in their own right -- as models of electric conduction in materials -- but also through their connection to certain natural Markov chains and random fields in probability theory. The goal of my talk is to introduce these connections and then discuss specific probabilistic limit theorems that can be derived for these objects. In particular, some basic methods of probabilistic homogenization theory will be shown and numerous related open questions brought up. |