## Electronic Journal of Probability

### Directed random walk on the backbone of an oriented percolation cluster

#### 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

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

Rights

#### 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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