Nadine Guillotin-Plantard and Arnaud Le Ny
Transient random walks on 2d oriented lattices
(316K, pdf)

ABSTRACT.  We study the asymtotic behavior of the simple random walk on oriented versions of $\mathbb{Z}^2$. The considered lattices are directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose distributions are generated by a dynamical system. We find a sufficient condition on the smoothness of the generation for the transience of the simple rnadom walk on almost every such oriented lattices, and as an illustration we provide a wide class of exemples of inhomogeneous or correlated distributions of the orientations. For ergodic dynamical systems, we also solve an open problem and prove a functional limit theorem in a corresponding space D of cadlag functions, with an unconventional normalization.