Abstract for the talk at 05.05.2015 (15:15 h)Oberseminar ANALYSIS - PROBABILITY
Alexandre Stauffer (University of Bath)
Random walk on dynamical percolation
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 \mu. 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 \mu 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 n^2/\mu. We also obtain results concerning mean squared displacement and hitting times. This is a joint work with Yuval Peres and Jeff Steif.