Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 531-548 (2004)

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Asymptotic mean values of Gaussian polytopes

Daniel Hug, G{ö}tz Olaf Munsonius and Matthias Reitzner

Mathematisches Institut, Albert-Ludwigs-Universit{ä}t, Eckerstr. 1, D-79104 Freiburg i. Br., Germany, e-mail:, e-mail:; Institut f{ü}r Analysis und Technische Mathematik, Technische Universit{ä}t Wien, Wiedner Hauptstrasse 8--10, A-1040 Vienna, Austria, e-mail:

Abstract: We consider geometric functionals of the convex hull of normally distributed random points in Euclidean space $\R^d$. In particular, we determine the asymptotic behaviour of the expected value of such functionals and of related geometric probabilities, as the number of points increases.

Keywords: Random points, convex hull, $f$-vector, geometric probability, normal distribution, Gaussian sample, Stochastic Geometry

Classification (MSC2000): 52A22, 60D05; 52B11, 62H10

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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.

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