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

Abstract

We sharpen ellipticity criteria for random walks in i.i.d. random environments introduced by Campos and Ram\'ırez 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 Ram\'ırez. 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.

Published at http://dx.doi.org/10.3150/14-BEJ683 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

• Cycle density in infinite Ramanujan graphs

Cited by in corpus (3)

• Local trapping for elliptic random walks in random environments in ${\mathbb{Z}}^d$
• Limit Theorem for sub-ballistic random walks in Dirichlet environment in dimension $d\ge 3$
• Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment