Monatshefte für Mathematik

, Volume 145, Issue 4, pp 307-319

First online:

Sylvester’s Problem for Symmetric Convex Bodies and Related Problems

  • Mark W. MeckesAffiliated withStanford University

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We consider moments of the normalized volume of a symmetric or nonsymmetric random polytope in a fixed symmetric convex body. We investigate for which bodies these moments are extremized, and calculate exact values in some of the extreme cases. We show that these moments are maximized among planar convex bodies by parallelograms.

2000 Mathematics Subject Classifications: 52A40; 52A22, 60D05
Key words: Sylvester’s problem, volumes of random polytopes, linear parameter systems