Gaussian samples, regular simplices, and exchangeability
type: Item
instance of: scholarly article
title: Gaussian samples, regular simplices, and exchangeability
zbMATH Open document ID: 0897.60012
DOI: 10.1007/PL00009292
author: O. Diekmann
published in: Discrete \& Computational Geometry
publication date: 1998-09-30T00:00:00Z
review text: Goodman and Pollack suggested the following mechanism for generating a random point set in Euclidean space: fix a (determined) finite set, randomly rotate it, and then project the result onto a lower dimensional space. This model was studied by \textit{F. Affentranger} and \textit{R. Schneider} [ibid. 7, No. 3, 219-226 (1992; Zbl 0751.52002)], who observed that the expected number of facets of the resulting polytope coincides with that of the convex hull of an appropriate i.i.d. Gaussian sample. This phenomenon was explained by the author and the reviewer [ibid. 11, No. 2, 141-147 (1994; Zbl 0795.52002)] by showing affine equivalence of the two mechanisms. The present paper establishes in a certain sense that the Gaussian sample model uniquely yields the Goodman-Pollack model.
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 52A22
zbMATH DE Number: 1011308
zbMATH Keywords: mechanism for generating a random point set
zbMATH Keywords: Gaussian sample model
zbMATH Keywords: Goodman-Pollack model
reviewed by: Richard A. Vitale
MaRDI profile type: Publication
cites work: Random projections of regular simplices
cites work: Q3675249
cites work: Regular simplices and Gaussian samples
cites work: A dozen de Finetti-style results in search of a theory
cites work: Sur L'enveloppe convexe des nuages de points aleatoires dans Rn. I
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description: scientific article; zbMATH DE number 1011308