Random oriented trees: A model of drainage networks
By S. Gangopadhyay, Rahul Roy, A. Sarkar. 2004
53 citations recorded by the source corpus.
Consider the d-dimensional lattice Ζ 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 co-ordinates 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≥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 ν and (b) the number of edges of a fixed length l.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/bccf79d60704f5994aa5e28777237a88149dda27
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In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- The Brownian Web: Characterization and Convergence (2003, unknown): “That is, by the Donsker invariance principle [10], the distribution ofY (δ)0,0 on the space of continuous paths converges asδ → 0 to standard Wiener measure.”
- The Radial Spanning Tree of a Poisson Point Process (2007, background): “An interesting question along the line of [12] and [15] is whether the directed spanning forest is almost surely a tree, namely, whether two sequences of ancestors coalesce almost surely (in dimension 2 and 3).”