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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064305

Digital Object Identifier
doi:10.1214/EJP.v18-2302

Mathematical Reviews number (MathSciNet)
MR3101646

Zentralblatt MATH identifier
1326.60142

Subjects
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]

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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