Asymptotic direction of random walks in Dirichlet environment

Laurent Tournier (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

In this 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. In addition, we identify the exact value or distribution of certain probabilities, answering and generalizing a conjecture of [SaTo10].

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-00701968v2⟩