Recurrence for persistent random walks in two dimensions

Details Recurrence for persistent random walks in two dimensions Recurrence for persistent random walks in two dimensions

2005-07-20

arxiv.org/abs/math/0507411v1

Stoch. Dyn. 7 (2007), no. 1, 53-74

Mathematics

Probability

20 pages, 7 figures

Scientific paper

10.1142/S0219493707001937

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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