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. |