Birkner M, Cerny J, Depperschmidt A, Gantert N (2013)
Publication Type: Journal article, Original article
Publication year: 2013
Book Volume: 18
Article Number: 80
DOI: 10.1214/EJP.v18-2302
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.
APA:
Birkner, M., Cerny, J., Depperschmidt, A., & Gantert, N. (2013). Directed random walk on the backbone of an oriented percolation cluster. Electronic Journal of Probability, 18. https://dx.doi.org/10.1214/EJP.v18-2302
MLA:
Birkner, Matthias, et al. "Directed random walk on the backbone of an oriented percolation cluster." Electronic Journal of Probability 18 (2013).
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