Random oriented trees: A model of drainage networks
成果类型：
Article
署名作者：
Gangopadhyay, S; Roy, R; Sarkar, A
署名单位：
Indian Statistical Institute; Indian Statistical Institute Kolkata; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Delhi
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051604000000288
发表日期：
2004
页码：
1242-1266
关键词：
摘要：
Consider the d-dimensional lattice Z(d) where each vertex is open or closed with probability p or 1 - p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth coordinates of v and w satisfy w(d) = v(d) - 1. In case of nonuniqueness of such a vertex w, we choose any one of the closest vertices with equal probability and independently of the other random mechanisms. It is shown that this random graph is a tree almost surely for d = 2 and 3 and it is an infinite collection of distinct trees for d greater than or equal to 4. In addition, for any dimension, we show that there is no bi-infinite path in the tree and we also obtain central limit theorems of (a) the number of vertices of a fixed degree v and (b) the number of edges of a fixed length l.