Random walks on FKG-horizontally oriented lattices

2003/03/05 by Nadine Guillotin‐Plantard, Nadine Guillotin-Plantard, Guillotin-Plantard, Nadine +2
Mathematics · #60F17 #60K35 #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60F17 #msc:60K35 #msc:60K37

paper · pdf · doi:10.48550/arxiv.math/0303063

16 pages

arxiv created 2003/03/05 · openalex publication_date 2003/03/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of the simple random walk on oriented version of ℤ². The considered latticesare not directed on the vertical axis but unidirectional on the horizontal one, with symmetric random orientations which are positively correlated. We prove that the simple random walk is transient and also prove a functionnal limit theorem in the space of cadlag functions, with an unconventional normalization.

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