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.
Recurrence for persistent random walks in two dimensions / M. Lenci. - In: STOCHASTICS AND DYNAMICS. - ISSN 0219-4937. - STAMPA. - 7:(2007), pp. 53-74. [10.1142/S0219493707001937]
Recurrence for persistent random walks in two dimensions
LENCI, MARCO
2007
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.