Small-ball probabilities for the volume of random convex sets
type: Item
instance of: scholarly article
title: Small-ball probabilities for the volume of random convex sets
zbMATH Open document ID: 1273.52007
author: Grigoris Paouris
author: Peter Pivovarov
published in: Discrete \& Computational Geometry
publication date: 2013-06-07T00:00:00Z
review text: 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.
reviewed by: Joscha Prochno
Mathematics Subject Classification ID: 52A22
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 6171521
zbMATH Keywords: volume of random sets
zbMATH Keywords: small deviations
zbMATH Keywords: rearrangements
zbMATH Keywords: affine quermassintegrals
MaRDI profile type: Publication
full work available at URL: s00454-013-9492-2
OpenAlex ID: W2015826142
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Small-ball probabilities for the volume of random convex sets (DOI)
DOI: 10.1007/S00454-013-9492-2