ON THE MONOTONICITY OF THE MOMENTS OF VOLUMES OF RANDOM SIMPLICES

Autor(en): Reichenwallner, Benjamin
Reitzner, Matthias 
Stichwörter: Mathematics; Mathematics, Applied; SIMPLEX
Erscheinungsdatum: 2016
Herausgeber: LONDON MATH SOC
Journal: MATHEMATIKA
Volumen: 62
Ausgabe: 3
Startseite: 949
Seitenende: 958
Zusammenfassung: 
In a d-dimensional convex body K random points X-0, . . . , 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. 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. Mathematika 58 (2012), 77-91], it is shown that moments of the volume of random simplices are, in general, not monotone under set inclusion.
ISSN: 00255793
DOI: 10.1112/S0025579316000127

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