Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21995
Barbour, A D; Xia, A (2001). The number of two-dimensional maxima. Advances in Applied Probability, 33(4):727-750.
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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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| DDC: | 510 Mathematics |
| Uncontrolled Keywords: | Maximal points; Stein's method; record values; Johnson-Mehl process |
| Language: | English |
| Date: | 2001 |
| Deposited On: | 07 Apr 2010 14:26 |
| Last Modified: | 23 Nov 2012 15:18 |
| Publisher: | Applied Probability Trust |
| ISSN: | 0001-8678 |
| Publisher DOI: | 10.1239/aap/1011994025 |
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