Student Working Seminar in Groups and Dynamics

Date: July 17, 2019

Time: 12:30PM - 1:30PM

Location: BLOC 624

Speaker: James O'Quinn

Title: Ergodic Theory on Stationary Random Graphs

Abstract: This is an expository talk on the paper "Ergodic Theory on Stationary Random Graphs" by Itai Benjamini and Nicolas Curien. In the 80's, Kaimonavich and Vershik explored the connection between asymptotic properties of random walks on groups and entropy theory. Stationary random graphs are a generalization of Cayley graphs where the stationary condition is a replacement for the homogeneity inherent in Cayley graphs, so that the connections developed by Kaimonavich and Vershik hold for random walks in this setting. I plan to give background on the results from the group setting as well as define stationary random graphs. The goal is to show that stationary random graphs of subexponential growth have the Liouville property.