Small-Ball Probabilities for the Volume of Random Convex Sets

Abstract

We prove small-deviation estimates for the volume of random convex sets. The focus is on convex hulls and Minkowski sums of line segments generated by independent random points. The random models considered include (Lebesgue) absolutely continuous probability measures with bounded densities and the class of log-concave measures. © 2013 Springer Science+Business Media New York.