Random walk on dynamical percolation

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


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.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss