Extremes on Trees

Details Extremes on Trees Extremes on Trees

2005-03-25

arxiv.org/abs/math/0503603v1

Annals of Probability 2005, Vol. 33, No. 1, 413-444

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000001008 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000001008

This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X_1,...,X_{N_n} where X_1,X_2,... are i.i.d. in \Re^2 with distribution F and N_n is independent of the X_i and satisfies N_n/n\to_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.

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