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The number of two-dimensional maxima

Published online by Cambridge University Press:  01 July 2016

A. D. Barbour*
Affiliation:
Universität Zürich
A. Xia*
Affiliation:
University of Melbourne
*
Postal address: Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland. Email address: [email protected]
∗∗ Postal address: Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010, Australia.

Abstract

Let n points be placed uniformly at random in a subset A of the plane. A point is said to be maximal in the configuration if no other point is larger in both coordinates. We show that, for large n and for many sets A, the number of maximal points is approximately normally distributed. The argument uses Stein's method, and is also applicable in higher dimensions.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 2001 

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Footnotes

Partly supported by Schweizerischer Nationalfondsprojekte 20-50686.97 and 20-61753.00.

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