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The number of two-dimensional maxima
Part of
A. D. Barbour, A. Xia
Journal:

Advances in Applied Probability / Volume 33 / Issue 4 / December 2001

Published online by Cambridge University Press:

01 July 2016, pp. 727-750

Print publication:

December 2001
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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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The number of two-dimensional maxima