@inproceedings{AddarioBerry2005TheSR,
title={The simple random walk on a random Voronoi tiling},
author={Louigi Addario-Berry and A Sarkar},
year={2005}
}

Let P be a Poisson point process in Rd with intensity 1. We show that the simple random walk on the cells of the Voronoi diagram of P is almost surely recurrent in dimensions d = 1 and d = 2 and is almost surely transient in dimension d ≥ 3.