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Random directed trees and forest - drainage networks with dependence


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Random directed trees and forest - drainage networks with dependence
 
2. Creator Author's name, affiliation, country Siva R Athreya; Indian Statistical Institute, Bangalore
 
2. Creator Author's name, affiliation, country Rahul Roy; Indian Statistical Institute, Delhi
 
2. Creator Author's name, affiliation, country Anish Sarkar; Indian Statistical Institute, Delhi
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random Graph, Random Oriented Trees, Random Walk
 
3. Subject Subject classification 0505C80, 60K35
 
4. Description Abstract Consider the $d$-dimensional lattice $\mathbb Z^d$ 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$ in the $45^\circ$ (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 $d \geq 4$. In addition, for any dimension, we show that there is no bi-infinite path in the tree.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Centre for Scientific and Industrial Research, India Grant-in-aid Scheme and Department of Science and Technology, India
 
7. Date (YYYY-MM-DD) 2008-12-01
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/580
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-580
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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