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Recurrence for persistent random walks in two dimensions

Marco Lenci
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Abstract

We discuss the question of recurrence for persistent, or Newtonian, random walks in Z^2, i.e., random walks whose transition probabilities depend both on the walker's position and incoming direction. We use results by Toth and Schmidt-Conze to prove recurrence for a large class of such processes, including all "invertible" walks in elliptic random environments. Furthermore, rewriting our Newtonian walks as ordinary random walks in a suitable graph, we gain a better idea of the geometric features of the problem, and obtain further examples of recurrence.

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Marco Lenci. 2005-07-20. Recurrence for persistent random walks in two dimensions. https://doi.org/10.1142/s0219493707001937

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