Directed random walk on the backbone of an oriented percolation cluster
Probability
2013-06-18 v3
Abstract
We consider a directed random walk on the backbone of the infinite 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) using a regeneration approach. Furthermore, we obtain a quenched central limit theorem (i.e.\ for almost any realisation of the cluster) via an analysis of joint renewals of two independent walks on the same cluster.
Cite
@article{arxiv.1204.2951,
title = {Directed random walk on the backbone of an oriented percolation cluster},
author = {Matthias Birkner and Jiri Cerny and Andrej Depperschmidt and Nina Gantert},
journal= {arXiv preprint arXiv:1204.2951},
year = {2013}
}
Comments
Replaced by revised version. Title changed slightly. 43 pages, 2 figures