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The number of two-dimensional maxima


Barbour, A D; Xia, A (2001). The number of two-dimensional maxima. Advances in Applied Probability, 33(4):727-750.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Maximal points; Stein's method; record values; Johnson-Mehl process
Language:English
Date:2001
Deposited On:07 Apr 2010 12:26
Last Modified:06 Dec 2017 20:52
Publisher:Applied Probability Trust
ISSN:0001-8678
Publisher DOI:https://doi.org/10.1239/aap/1011994025

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