Directed random walk on the backbone of an oriented percolation cluster

Birkner M, Cerny J, Depperschmidt A, Gantert N (2013)

Publication Type: Journal article, Original article

Publication year: 2013

Journal

Electronic Journal of Probability Institute of Mathematical Statistics (IMS): OAJ / Institute of Mathematical Statistics

Book Volume: 18

Article Number: 80

DOI: 10.1214/EJP.v18-2302

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.

Authors with CRIS profile

Andrej Depperschmidt

Involved external institutions

Albert-Ludwigs-Universität Freiburg DE Germany (DE) Technische Universität München (TUM) DE Germany (DE) Johannes Gutenberg-Universität Mainz (JGU) DE Germany (DE) Medizinische Universität Wien AT Austria (AT)

How to cite

APA:

Birkner, M., Cerny, J., Depperschmidt, A., & Gantert, N. (2013). Directed random walk on the backbone of an oriented percolation cluster. Electronic Journal of Probability, 18. https://dx.doi.org/10.1214/EJP.v18-2302

MLA:

Birkner, Matthias, et al. "Directed random walk on the backbone of an oriented percolation cluster." Electronic Journal of Probability 18 (2013).

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