Directed random walk on the backbone of an oriented percolation cluster

@article{Birkner2012DirectedRW,
  title={Directed random walk on the backbone of an oriented percolation cluster},
  author={Matthias C. F. Birkner and Jiř{\'i} {\vC}ern{\'y} and Andrej Depperschmidt and Nina Gantert},
  journal={Electronic Journal of Probability},
  year={2012},
  volume={18},
  pages={1-35}
}
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… 

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