# Recurrence for persistent random walks in two dimensions

@article{Lenci2007RecurrenceFP,
title={Recurrence for persistent random walks in two dimensions},
author={Marco Lenci},
journal={Stochastics and Dynamics},
year={2007},
volume={07},
pages={53-74}
}
• M. Lenci
• Published 20 July 2005
• Mathematics
• Stochastics and Dynamics
We discuss the question of recurrence for persistent, or Newtonian, random walks in ℤ2, 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…
10 Citations

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