Bhatt, Abhay G. ; Roy, Rahul (2004) On a random directed spanning tree Advances in Applied Probability, 36 (1). pp. 19-42. ISSN 0001-8678
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Official URL: http://projecteuclid.org/euclid.aap/1077134462
Related URL: http://dx.doi.org/10.1239/aap/1077134462
Abstract
We study the asymptotic properties of a minimal spanning tree formed by n points uniformly distributed in the unit square, where the minimality is amongst all rooted spanning trees with a direction of growth. We show that the number of branches from the root of this tree, the total length of these branches, and the length of the longest branch each converges weakly. This model is related to the study of record values in the theory of extreme-value statistics and this relation is used to obtain our results. The results also hold when the tree is formed from a Poisson point process of intensity n in the unit square.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Applied Probability Trust. |
| Keywords: | Minimal Spanning Tree; Record Values; Weak Convergence |
| ID Code: | 72335 |
| Deposited On: | 29 Nov 2011 13:39 |
| Last Modified: | 29 Nov 2011 13:39 |
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