Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 45, No. 2, pp. 531-548 (2004)
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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 polytopesDaniel Hug, G{ö}tz Olaf Munsonius and Matthias ReitznerMathematisches Institut, Albert-Ludwigs-Universit{ä}t, Eckerstr. 1, D-79104 Freiburg i. Br., Germany, e-mail: daniel.hug@math.uni-freiburg.de, e-mail: olaf@munsonius.de; Institut f{ü}r Analysis und Technische Mathematik, Technische Universit{ä}t Wien, Wiedner Hauptstrasse 8--10, A-1040 Vienna, Austria, e-mail: Matthias.Reitzner+e1142@tuwien.ac.atAbstract: 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 Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
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