05-250 Marco Lenci

Recurrence for persistent random walks in two dimensions (139K, LaTeX 2e with 7 eps figures) Jul 20, 05

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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.

Files: 05-250.src( 05-250.comments , 05-250.keywords , rwlg-arc.tex , fig-rwlg-1.eps , fig-rwlg-2.eps , fig-rwlg-3.eps , fig-rwlg-4.eps , fig-rwlg-5.eps , fig-rwlg-6.eps , fig-rwlg-7.eps )