Transient random walks on 2d-oriented lattices

Nadine Guillotin-Plantard; Arnaud Le Ny

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Transient random walks on 2d-oriented lattices

Nadine Guillotin-Plantard·Arnaud Le Ny

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Abstract

We study the asymptotic behavior of the simple random walk on oriented versions of $\mathbb{Z}^2$. The considered lattices are not 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 random walk on almost every such oriented lattices, and as an illustration we provide a wide class of examples of inhomogeneous or correlated distributions of the orientations. For ergodic dynamical systems, we also prove a strong law of large numbers and, in the particular case of i.i.d. orientations, we 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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BibTeX RIS

Nadine Guillotin-Plantard, Arnaud Le Ny. 2006-01-05. Transient random walks on 2d-oriented lattices. https://arxiv.org/abs/math/0601102

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