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2013 Directed random walk on the backbone of an oriented percolation cluster
Matthias Birkner, Jiri Cerny, Andrej Depperschmidt, Nina Gantert
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Electron. J. Probab. 18: 1-35 (2013). 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.


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Matthias Birkner. Jiri Cerny. Andrej Depperschmidt. Nina Gantert. "Directed random walk on the backbone of an oriented percolation cluster." Electron. J. Probab. 18 1 - 35, 2013.


Accepted: 31 August 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1326.60142
MathSciNet: MR3101646
Digital Object Identifier: 10.1214/EJP.v18-2302

Primary: 60K37
Secondary: 60J10 , 60K35 , 82B43

Keywords: central limit theorem in random environment , Dynamical random environment , Oriented percolation , Random walk , supercritical cluster

Vol.18 • 2013
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