Directed random walk on an oriented percolation cluster

Details Directed random walk on an oriented percolation cluster Directed random walk on an oriented percolation cluster

2012-04-13

arxiv.org/abs/1204.2951v1

Mathematics

Probability

30 pages, 2 figures

Scientific paper

We consider directed random walk on the infinite percolation cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the `ancestral lineage' of an individual in the stationary discrete-time contact process. We prove a law of large numbers and an annealed central limit theorem (i.e., averaged over the realisations of the cluster) with a regeneration approach. Via an analysis of joint renewals of two independent walks on the same cluster, we obtain furthermore a quenched central limit theorem (i.e. for almost any realisation of the cluster) in dimensions $1+d$ with $d\geq 2$.

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