Abstract
We study the asymptotic behavior of the simple random walk on oriented versions of ${\bf Z}^2$. 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 independent identically distributed orientations, we solve an open problem and prove a functional limit theorem in the space ${\cal D}([0,\infty[,{\bf R}^2)$ of càdlàg functions, with an unconventional normalization.
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