Article contents
ON THE MONOTONICITY OF THE EXPECTED VOLUME OF A RANDOM SIMPLEX
Published online by Cambridge University Press: 20 June 2011
Abstract
Consider a random simplex in a d-dimensional convex body which is 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 such a random simplex monotone non-decreasing under inclusion? We show that this is true when d is 1 or 2, but does not hold for 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.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 2012
References
- 9
- Cited by