EUDML | Expectation of Random Polytopes.

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Displaying similar documents to “Expectation of Random Polytopes.”

Recent Results on Random Polytopes

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.

Intrinsic volumes and f-vectors of random polytopes.

Imre Bárány (1989)

Mathematische Annalen

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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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Random Polytopes in the d- Dimensional Cube.

Z. Füredi (1986)

Discrete & computational geometry

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Random polytopes in a convex polytope, independence of shape, and concentration of vertices.

Imre Bárány, Christian Buchta (1993)

Mathematische Annalen

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Random polytopes and the volume-product of symmetric convex bodies.

Shlomo Reisner (1985)

Mathematica Scandinavica

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Flexible cross-polytopes in the Euclidean 4-space.

Stachel, Hellmuth (2000)

Journal for Geometry and Graphics

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A purely combinatorial proof of the Hadwiger Debrunner $(p, q)$ conjecture.

Alon, N., Kleitman, D.J. (1997)

The Electronic Journal of Combinatorics [electronic only]

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The Mayer-Vietoris and IC Equations for Convex Polytopes.

J. Fine (1995)

Discrete & computational geometry

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Two Poset Polytopes.

R.P. Stanley (1986)

Discrete & computational geometry

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On simple polytopes.

Peter McMullen (1993)

Inventiones mathematicae

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Exterior Algebra and Projections of Polytopes.

P. Filliman (1990)

Discrete & computational geometry

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On a certain class of polytopes associated with independence systems.

A.B. Hansen (1977)

Mathematica Scandinavica

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