Directed random walk on the backbone of an oriented percolation cluster
Directed random walk on the backbone of an oriented percolation cluster
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DOI：
10.1214/ejp.v18-2302
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发表时间：
2012-04
影响因子：
1.4
通讯作者：
M. Birkner;J. Černý;A. Depperschmidt;N. Gantert
中科院分区：
文献类型：
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作者：
M. Birkner;J. Černý;A. Depperschmidt;N. Gantert
我们考虑一个有向随机行走的骨干上的无限集群产生的超临界定向渗流，或等价的时空嵌入的“祖先血统”的一个人在静态离散时间接触过程。我们证明了一个大数定律和一个退火中心极限定理（即，在集群的实现上平均）。此外，我们得到了淬火中心极限定理（即几乎任何实现的集群）通过分析联合更新的两个独立的行走在同一集群。
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.