Small-ball probabilities for the volume of random convex sets
The authors prove several interesting small-deviation estimates for the volume of random convex sets in \(\mathbb R^n\). Typical models involve convex hulls or Minkowski sums of line segments generated by independent random points. The random models considered include absolutely continuous probability measures (wrt Lebesgue measure) with bounded densities and the class of log-concave measures. The proofs are quite technical and involved.
scientific article; zbMATH DE number 6171521
scientific article