Talk

Random walk on dynamical percolation

  • Alexandre Stauffer (University of Bath)
G3 10 (Lecture hall)

Abstract

We study the behavior of random walk on dynamical percolation, which is a random walk that moves in an environment (graph) that changes over time. In this model, the edges of a graph G are either open or closed, and refresh their status at rate μ. At the same time a random walker moves on G at rate 1 but only along edges which are open. The regime of interest here is when μ goes to zero as the number of vertices of G goes to infinity, since this creates long-range dependencies on the model. When G is the d-dimensional torus of side length n, we prove that in the subcritical regime, the mixing times is of order n2μ. We also obtain results concerning mean squared displacement and hitting times. This is a joint work with Yuval Peres and Jeff Steif.