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ON THE MONOTONICITY OF THE MOMENTS OF VOLUMES OF RANDOM SIMPLICES

Part of: General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 June 2016

Benjamin Reichenwallner  and
Matthias Reitzner
Benjamin Reichenwallner
Affiliation:
Fachbereich Mathematik, Universität Salzburg, Hellbrunnerstraße 34, 5020 Salzburg, Austria email benjamin.reichenwallner@sbg.ac.at
Matthias Reitzner
Affiliation:
Institut für Mathematik, Universität Osnabrück, Albrechtstr. 28a, D-49076 Osnabrück, Germany email matthias.reitzner@uni-osnabrueck.de
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Abstract

In a $d$ -dimensional convex body $K$ random points $X_{0},\ldots ,X_{d}$ are chosen. Their convex hull is a random simplex. The expected volume of a random simplex is monotone under set inclusion if $K\subset L$ implies that the expected volume of a random simplex in $K$ is smaller than the expected volume of a random simplex in $L$ . Continuing work of Rademacher [On the monotonicity of the expected volume of a random simplex. Mathematika58 (2012), 77–91], it is shown that moments of the volume of random simplices are, in general, not monotone under set inclusion.

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry

Information

Type
Research Article
Information
Mathematika , Volume 62 , Issue 3 , 2016 , pp. 949 - 958
Copyright
Copyright © University College London 2016 

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