Electronic Journal of Probability

Directed random walk on the backbone of an oriented percolation cluster

Matthias Birkner, Jiri Cerny, Andrej Depperschmidt, and Nina Gantert

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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.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 80, 35 pp.

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

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Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 82B43: Percolation [See also 60K35] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Random walk dynamical random environment oriented percolation supercritical cluster central limit theorem in random environment

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Birkner, Matthias; Cerny, Jiri; Depperschmidt, Andrej; Gantert, Nina. Directed random walk on the backbone of an oriented percolation cluster. Electron. J. Probab. 18 (2013), paper no. 80, 35 pp. doi:10.1214/EJP.v18-2302. https://projecteuclid.org/euclid.ejp/1465064305

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