Statistics Seminars: Random Oriented Trees: A Model of Drainage Networks
11 October 2002 00:00 in CM221
"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 co-ordinates of v and w satisfy w(d) = v(d) -1. 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 or 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.
"Indian Statistical Institute, New Delhi"
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