This is an announcement for the paper "On the monotonicity of the expected volume of a random simplex" by Luis Rademacher.

Abstract: Let a random simplex in a d-dimensional convex body be the convex hull of d+1 random points from the body. We study the following question: As a function of the convex body, is the expected volume of a random simplex monotone non-decreasing under inclusion? We show that this holds if d is 1 or 2, and does not hold if d >= 4. We also prove similar results for higher moments of the volume of a random simplex, in particular for the second moment, which corresponds to the determinant of the covariance matrix of the convex body. These questions are motivated by the slicing conjecture.

Archive classification: math.PR math.FA math.MG

Submitted from: lrademac@cse.ohio-state.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1008.3944

or

http://arXiv.org/abs/1008.3944