Directed random walk on the backbone of an oriented percolation cluster

2012/04/13 by Matthias Birkner, Birkner, Matthias, Cerny, Jiri +4
Mathematics · Physics and Astronomy · #60J10 #60K35 #60K37 #82B43 #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1204.2951

openalex publication_date 2012/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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