## The Annals of Probability

### Extremes on trees

#### Abstract

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/np1. 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.

#### Article information

Source
Ann. Probab., Volume 33, Number 1 (2005), 413-444.

Dates
First available in Project Euclid: 11 February 2005

https://projecteuclid.org/euclid.aop/1108141730

Digital Object Identifier
doi:10.1214/009117904000001008

Mathematical Reviews number (MathSciNet)
MR2118869

Zentralblatt MATH identifier
1096.60009

#### Citation

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

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