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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 34 open journal systems 


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

Nadine Guillotin-Plantard, Université Lyon 1
Arnaud Le Ny, Université Paris Sud


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.


Full text: PDF

Pages: 337-351

Published on: June 20, 2008
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Electronic Communications in Probability. ISSN: 1083-589X