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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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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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||Maximal points; Stein's method; record values; Johnson-Mehl process|
|Deposited On:||07 Apr 2010 12:26|
|Last Modified:||23 Nov 2012 14:18|
|Publisher:||Applied Probability Trust|
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