The Smallest Parallelepiped of n Random Points and Peeling

Ju¨rg Hu¨sler ()
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Ju¨rg Hu¨sler: University of Bern

Methodology and Computing in Applied Probability, 2000, vol. 2, issue 2, 169-181

Abstract: Abstract Let n random points be given with uniform distribution in the d-dimensional unit cube [0,1]d. The smallest parallelepiped A which includes all the n random points is dealt with. We investigate the asymptotic behavior of the volume of A as n tends to ∞. Using a point process approach, we derive also the asymptotic behavior of the volumes of the k-th smallest parallelepipeds A n (k) which are defined by iteration. Let A n = A n (1) . Given A n (k,-,1) delete the random points X i which are on the boundary ∂A n (k,-,1) , and construct the smallest parallelepiped which includes the inner points of A n (k,-,1) , this defines A n (k) . This procedure is known as peeling of the parallelepiped An.

Keywords: parallelepiped; peeling; volume; limit distribution; point process (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1010098023091

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