Sharp ellipticity conditions for ballistic behavior of random walks in random environment

Élodie Bouchet (1) , Alejandro F. Ramirez (2) , Christophe Sabot (1)

1 ICJ - Institut Camille Jordan
2 Departamento de Matemáticas [Santiago de Chile]

We sharpen the ellipticity criteria for random walks in i.i.d. random environments introduced by Campos and Ramírez which ensure ballistic behavior. Furthermore, we construct new examples of random environments for which the walk satisfies the polynomial ballisticity criteria of Berger, Drewitz and Ramírez. As a corollary we can exhibit a new range of values for the parameters of Dirichlet random environments in dimension $d=2$ under which the corresponding random walk is ballistic.

Mots clés: Random walk in random environment; Dirichlet distribution; Reinforced random walks; Max-flow min-cut theorem

Domaines: Probabilités [math.PR]

Élodie Bouchet, Alejandro F. Ramirez, Christophe Sabot. Sharp ellipticity conditions for ballistic behavior of random walks in random environment. 2013. ⟨hal-00876077v1⟩