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Directed random walk on the backbone of an oriented percolation cluster


 
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1. Title Title of document Directed random walk on the backbone of an oriented percolation cluster
 
2. Creator Author's name, affiliation, country Matthias Birkner; Johannes-Gutenberg-Universität Mainz; Germany
 
2. Creator Author's name, affiliation, country Jiri Cerny; University of Vienna; Austria
 
2. Creator Author's name, affiliation, country Andrej Depperschmidt; Albert-Ludwigs-Universität Freiburg; Germany
 
2. Creator Author's name, affiliation, country Nina Gantert; Technische Universität München; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walk, dynamical random environment, oriented percolation, supercritical cluster, central limit theorem in random environment
 
3. Subject Subject classification 60K37, 60J10, 82B43, 60K35
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) DFG
 
7. Date (YYYY-MM-DD) 2013-08-31
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2302
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2302
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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