TY - JOUR
T1 - Directed random walk on the backbone of an oriented percolation cluster
AU - Birkner, Matthias
AU - Černý, Jiří
AU - Depperschmidt, Andrej
AU - Gantert, Nina
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Central limit theorem in random environment
KW - Dynamical random environment
KW - Oriented percolation
KW - Random walk
KW - Supercritical cluster
UR - http://www.scopus.com/inward/record.url?scp=84883630404&partnerID=8YFLogxK
U2 - 10.1214/EJP.v18-2302
DO - 10.1214/EJP.v18-2302
M3 - Article
AN - SCOPUS:84883630404
SN - 1083-6489
VL - 18
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
M1 - 80
ER -