Minicourse on Random Resistor Networks

Abstract

A 2-week minicourse on the basic properties of random resistor networks on graphs. Covers Ohm’s and Kirchoff’s Laws, the Poisson equation, the Matrix-Tree Theorem, spanning trees, Wilson’s algorithm and the Burton-Pemantle theorem, and culminates with a summary of the Golden-Papanicolaou approach to network problems based on spectral theory.