Graduate Probability Seminar

Title: Random Walks and Electrical Networks

Abstract: Electrical networks provide a useful framework for studying reversible Markov chains. In this talk, we introduce the correspondence between random walks and electrical networks, interpreting voltages as hitting probabilities and currents as expected net edge crossings. We then relate effective resistance to escape probabilities and show that a random walk is transient precisely when the effective resistance to infinity is finite. Examples on paths and trees illustrate how network reduction simplifies probabilistic calculations.