A functional limit theorem for a 2D-random walk with dependent marginals

2007/05/23 by Nadine Guillotin-Plantard, Guillotin-Plantard, Nadine, Arnaud Le Ny +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.0705.3342

arxiv created 2007/05/23 · arxiv updated 2009/12/01

Abstract

We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional limit theorem, with a non-Gaussian horizontal behavior. We also prove that the horizontal and vertical components are not asymptotically independent.

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