The simple random walk on a random Voronoi tiling

  title={The simple random walk on a random Voronoi tiling},
  author={Louigi Addario-Berry and A Sarkar},
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. 

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