| Título: | Random directed trees and forest - drainage networks with dependence |
| Autores: |
Athreya, Siva R; Indian Statistical Institute, Bangalore Roy, Rahul; Indian Statistical Institute, Delhi Sarkar, Anish; Indian Statistical Institute, Delhi |
| Fecha: | 2008-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Random Graph, Random Oriented Trees, Random Walk 0505C80, 60K35 |
| Descripción: | 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. |
| Idioma: | No aplica |
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