The Annals of Probability
- Ann. Probab.
- Volume 33, Number 1 (2005), 413-444.
Extremes on trees
This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X1,…,XNn where X1,X2,… are i.i.d. in ℜ2 with distribution F and Nn is independent of the Xi and satisfies Nn/n→p1. A new approach based on spatial blocking and a locally orthogonal coordinate system is developed to treat cases for which F has unbounded support. The general results are applied to a number of special cases, including elliptically contoured distributions, distributions with independent Weibull-like margins and distributions with parallel level curves.
Ann. Probab., Volume 33, Number 1 (2005), 413-444.
First available in Project Euclid: 11 February 2005
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Hsing, Tailen; Rootzén, Holger. Extremes on trees. Ann. Probab. 33 (2005), no. 1, 413--444. doi:10.1214/009117904000001008. https://projecteuclid.org/euclid.aop/1108141730