Gaussian samples, regular simplices, and exchangeability
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.
mechanism for generating a random point set
scientific article; zbMATH DE number 1011308