### On the Convex Hull of Uniform Random Points in a Simple d-Polytope.

J.A. Wieacker, F. Affentranger (1991)

Discrete & computational geometry

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J.A. Wieacker, F. Affentranger (1991)

Discrete & computational geometry

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Juan Francisco Verdegay-López, Serafín Moral (2001)

Mathware and Soft Computing

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This paper studies the problem of marginalizing convex polytopes of probabilities represented by a set of constraints. This marginalization is obtained as a special case of projection on a specific subspace. An algorithm that projects a convex polytope on any subspace has been built and the expression of the subspace, where the projection must be made for obtaining the marginalization, has been calculated.

Thomas Kahle, Walter Wenzel, Nihat Ay (2009)

Kybernetika

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In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.

P. d&#039;Alessandro, M. Dalla Mora (1988)

RAIRO - Operations Research - Recherche Opérationnelle

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Rolf Schneider (2008)

Bollettino dell'Unione Matematica Italiana

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This is a survey over recent asymptotic results on random polytopes in d-dimensional Euclidean space. Three ways of generating a random polytope are considered: convex hulls of finitely many random points, projections of a fixed high-dimensional polytope into a random d-dimensional subspace, intersections of random closed halfspaces. The type of problems for which asymptotic results are described is different in each case.

Imre Bárány (1989)

Mathematische Annalen

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McMullen, Peter (1993)

Beiträge zur Algebra und Geometrie

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Deza, Michel, Dutour, Mathieu (2003)

Experimental Mathematics

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Ohsugi, Hidefumi, Hibi, Takayuki (2005)

The Electronic Journal of Combinatorics [electronic only]

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Bayer, Margaret M. (2004)

The Electronic Journal of Combinatorics [electronic only]

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Imre Bárány, Christian Buchta (1993)

Mathematische Annalen

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