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Stability results for the volume of random simplices
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 4, August 2014
- pp. 833-857
- 10.1353/ajm.2014.0030
- Article
- Additional Information
It is known that for a convex body $K$ in ${\Bbb R}^d$ of volume one, the expected volume of random simplices
in $K$ is minimized if $K$ is an ellipsoid, and for $d=2$, maximized if $K$ is a triangle. Here we provide
corresponding stability estimates.