Random walks on FKG-horizontally oriented lattices

Details Random walks on FKG-horizontally oriented lattices Random walks on FKG-horizontally oriented lattices

2003-03-05

arxiv.org/abs/math/0303063v1

Mathematics

Probability

16 pages

Scientific paper

We study the asymptotic behavior of the simple random walk on oriented version of $\mathbb{Z}^2$. 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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