# 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.

## Statistics

### Citations

13 citations in Web of Science®
10 citations in Scopus®