Integrability of exit times and ballisticity for random walks in Dirichlet environment.
Reversed Dirichlet environment and directional transience of random walks in Dirichlet environment
We consider random walks in a random environment given by i.i.d. Dirichlet distributions at each vertex of ℤ or, equivalently, oriented edge reinforced random walks on ℤ. The parameters of the distribution are a 2-uplet of positive real numbers indexed by the unit vectors of ℤ. We prove that, as soon as these weights are nonsymmetric, the random walk is transient in a direction (i.e., it satisfies ⋅ → +∞ for some ) with positive probability. In dimension 2, this result is strenghened...
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