The goal of the mini-course by Joe Chen is to describe the recent progress on establishing scaling limits of many-particle systems on state spaces which are bounded in the resistance metric, a.k.a. "resistance spaces." These include trees, fractals, and random graphs arising from critical percolation. As a concrete example, one can establish scaling limits of the weakly asymmetric exclusion process on the Sierpinski gasket interacting with 3 boundary reservoirs, which generalizes (in a nontrivial way) the analysis on the unit interval interacting with 2 boundary reservoirs.
The key ideas behind these results will be explained, and connections to the analysis of (S)PDEs, and issues of non-equilibrium statistical physics, on resistance spaces will be discussed. From a technical point of view, some novel functional inequalities for the exclusion process that relates to electrical resistance will be addressed, and the way they are used to effect "coarse-graining" in passing to the scaling limits will be described.