The number of two-dimensional maxima
A. D. Barbour, A. Xia · Advances in Applied Probability · 2001
Letnpoints be placed uniformly at random in a subsetAof 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 largenand for many setsA, the number of maximal points is approximately normally distributed. The argument uses Stein's method, and is also applicable in higher dimensions.