Transient random walk in with stationary orientations

Françoise Pene (1, 2)

1 UEB - Université européenne de Bretagne - European University of Brittany
2 UBO - Université de Brest

In this paper, we extend a result of Campanino and Pétritis [  (2003) 391–412]. We study a random walk in with random orientations. We suppose that the orientation of the th floor is given by , where is a stationary sequence of random variables. Once the environment fixed, the random walk can go either up or down or can stay in the present floor (but moving with respect to its orientation). This model was introduced by Campanino and Pétritis in [  (2003) 391–412] when the is a sequence of independent identically distributed random variables. In [  (2007) 815–826], Guillotin-Plantard and Le Ny extend this result to a situation where the orientations of the floors are independent but chosen with stationary probabilities (not equal to 0 and to 1). In the present paper, we generalize the result of [  (2003) 391–412] to some cases when is stationary. Moreover we extend slightly a result of [ (2007) 815–826].

Mots clés: Mathematics

Françoise Pene. Transient random walk in with stationary orientations. ESAIM: Probability and Statistics, 2009, 13, pp.417-436. ⟨10.1051/ps:2008019⟩. ⟨hal-00520010⟩