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2008 A functional limit theorem for a 2d-random walk with dependent marginals
Nadine Guillotin-Plantard, Arnaud Le Ny
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Electron. Commun. Probab. 13: 337-351 (2008). DOI: 10.1214/ECP.v13-1386


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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Nadine Guillotin-Plantard. Arnaud Le Ny. "A functional limit theorem for a 2d-random walk with dependent marginals." Electron. Commun. Probab. 13 337 - 351, 2008.


Accepted: 20 June 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60066
MathSciNet: MR2415142
Digital Object Identifier: 10.1214/ECP.v13-1386

Primary: 60F17
Secondary: 60G18 , 60K37

Keywords: random environments , random sceneries , Random walks

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