UBC Probability Seminar: Jonathan Hermon

  • Date: 02/08/2023
Jonathan Hermon, UBC

University of British Columbia


On the universality of fluctuations for the cover time


What is the structure of the set of the last few points visited by a random walk on a graph? We show that on vertex-transitive graphs of bounded degree, this set is decorrelated (it is close to a product measure in total variation) if and only if a simple geometric condition on the diameter of the graph holds. In this case, the cover time has universal fluctuations: properly scaled, this time converges to a Gumbel distribution. To prove this result we rely on recent progress in geometric group theory (about quantitative versions of Gromov's Theorem for finite vertex-transitive graphs) and we prove refined quantitative estimates showing that the hitting time of a small set of vertices is typically approximately an exponential random variable. This talk is based on joint work with Nathanaƫl Berestycki and Lucas Teyssier.

Other Information: 

Location: ESB 4127