06-4 Nadine Guillotin-Plantard and Arnaud Le Ny

Transient random walks on 2d oriented lattices (316K, pdf) Jan 5, 06

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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.

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