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The Simple Random Walk On A Random Voronoi Tiling, Amites Sarkar, Louigi Addario-Berry

Amites Sarkar

Let P be a Poisson point process in ℝ^d 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.