Reversed Dirichlet environment and directional transience of random walks in Dirichlet environment

@inproceedings{Sabot2010ReversedDE,
  title={Reversed Dirichlet environment and directional transience of random walks in Dirichlet environment},
  author={Christophe Sabot and Laurent Tournier},
  year={2010}
}
We consider random walks in a random environment given by i.i.d. Dirichlet distributions at each vertex of Zd or, equivalently, oriented edge reinforced random walks on Zd . The parameters of the distribution are a 2d-uplet of positive real numbers indexed by the unit vectors of Zd . We prove that, as soon as these weights are nonsymmetric, the random walk is transient in a direction (i.e., it satisfies Xn · →n +∞ for some ) with positive probability. In dimension 2, this result is strenghened… CONTINUE READING