Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4321
Title: A note on Sylvester's problem for random polytopes in a convex body
Authors: Campi, Stefano
Colesanti, Andrea
Gronchi, Paolo
Issue Date: 1999
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: S. Campi, A. Colesanti and P. Gronchi, "A note on Sylvester's problem for random polytopes in a convex body", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (1999), pp. 79-94.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (1999)
Abstract: 
For any d-dimensional convex body K of unit volume, d$\geq$2, let
M$_{r}$(K; n), r $\geq$ l, n$\geq$ d+ l, be the r-th order moment
of the volume of the convex hull of n random points from K. The paper
deals with the problem of determining maximizers of M$_{r}$ ( K;
n) in the class of all d-dimensional convex bodies of unit volume.
A method for selecting possible solutions, which is based on special
continuous movements of convex bodies, is presented. The results obtained
by this method support the conjecture that, for every r and n, the
only maximizers of M$_{r}$(K; n) are simplices.
Type: Article
URI: http://hdl.handle.net/10077/4321
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (1999)

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