2006/01/05 by Nadine Guillotin‐Plantard, Nadine Guillotin-Plantard, Guillotin-Plantard, Nadine +2
Mathematics · #60F17 #60K35 #60K37 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.DS #math.PR #msc:60F17 #msc:60K35 #msc:60K37
paper · pdf · doi:10.48550/arxiv.math/0601102
15 pages
arxiv created 2006/01/05 · openalex publication_date 2006/01/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the asymptotic behavior of the simple random walk on oriented versions of ℤ2. 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.