Random directed trees and forest - Drainage networks with dependence

Athreya, Siva R. ; Roy, Rahul ; Sarkar, Anish (2008) Random directed trees and forest - Drainage networks with dependence Electronic Journal of Probability, 13 . pp. 2160-2189. ISSN 1083-6489

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Official URL: http://128.208.128.142/~ejpecp/viewarticle.php?id=...

Abstract

Consider the d-dimensional lattice Zd 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 in the 45 ° (downward) light cone generated at v. In case of non-uniqueness 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 ≥ 4. In addition, for any dimension, we show that there is no bi-infinite path in the tree.

Item Type:Article
Source:Copyright of this article belongs to Institute of Mathematical Statistics.
Keywords:Random Graph; Random Oriented Trees; Random Walk
ID Code:72287
Deposited On:29 Nov 2011 13:39
Last Modified:29 Nov 2011 13:39

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