The number of two-dimensional maxima

A. D. Barbour, Aihua Xia

Type: Article

Publication Date: 2001-12-01

Citations: 28

DOI: https://doi.org/10.1239/aap/1011994025

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.

Locations

Advances in Applied Probability - View
Zurich Open Repository and Archive (University of Zurich) - View - PDF

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