6533b839fe1ef96bd12a5ac0

RESEARCH PRODUCT

Directed random walk on the backbone of an oriented percolation cluster

Jiri CernyNina GantertAndrej DepperschmidtMatthias Birkner

subject

Statistics and ProbabilityDiscrete mathematicsdynamical random environment82B43Probability (math.PR)Random walkRandom walksupercritical clusterddc:60K3760K37 60J10 82B43 60K35Mathematics::Probability60K35Percolationcentral limit theorem in random environmentContact process (mathematics)Cluster (physics)FOS: MathematicsEmbedding60J10Statistics Probability and UncertaintyMathematics - Probabilityoriented percolationMathematicsCentral limit theorem

description

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.

yearjournalcountryeditionlanguage
2012-04-13
10.1214/ejp.v18-2302https://mediatum.ub.tum.de/1662267