Asymptotic direction of random walks in Dirichlet environment

Laurent Tournier (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

In this short paper we generalize the result of directional transience from [SabotTournier10]. This enables us, by means of [Simenhaus07], [ZernerMerkl01] and [Bouchet12] to conclude that, on Z^d (for any dimension d), random walks in i.i.d. Dirichlet environment, or equivalently oriented-edge reinforced random walks, have almost-surely an asymptotic direction equal to the direction of the initial drift, unless this drift is zero.

Mots clés: Random walks in random environment; Dirichlet environment; reinforced random walks; asymptotic direction; directional transience; time reversal

Domaines: Probabilités [math.PR]

Laurent Tournier. Asymptotic direction of random walks in Dirichlet environment. 2012. ⟨hal-00701968v1⟩