An introduction to the scaling limits of random walks via the resistance metric
Visiting Scholar David Croydon will present a series of 4 lectures (Mondays 1pm-2pm) on this theme, aimed at graduate students.
The connections between electricity and probability are deep, and have provided many tools for understanding the behaviour of stochastic processes. In this course, I will introduce the basic connections between electrical networks and random walks, and go on to describe some recent work that applies these techniques to understanding random walks on various examples of random graphs. In particular, I will explain how the resistance metric is a natural way in which to encode information about and derive scaling limits for random walks on graphs with a large scale fractal structure. Of particular interest are random graphs in critical regimes (e.g. critical Galton-Watson trees, uniform spanning trees, or critical percolation clusters), where such large-scale fractal behaviour occurs naturally. I will also describe how the results shed light on time-changed random walks, such as the Bouchaud trap model, in which the holding times at vertices have a random distribution.
Professor David Croydon, Kyoto University