For any d-dimensional convex body K of unit volume, let Mr(K;n) 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 Mr(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 Mr(K;n) are simplices.

Campi, S., Colesanti, A., Gronchi, P. (1999). A note on Sylvester problem for random polytopes in a convex body. RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE, 31, 79-94.

A note on Sylvester problem for random polytopes in a convex body

CAMPI, STEFANO;
1999-01-01

Abstract

For any d-dimensional convex body K of unit volume, let Mr(K;n) 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 Mr(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 Mr(K;n) are simplices.
1999
Campi, S., Colesanti, A., Gronchi, P. (1999). A note on Sylvester problem for random polytopes in a convex body. RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE, 31, 79-94.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/22050
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