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A functional limit theorem for a 2D-random walk with dependent marginals. (English) Zbl 1189.60066

Summary: 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.

MSC:

60F17 Functional limit theorems; invariance principles
60K37 Processes in random environments
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