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International Conference on Geometric Science of Information

GSI 2015: Geometric Science of Information pp 195–202Cite as

Asymptotic Properties of Random Polytopes

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

Abstract

Random polytopes have constituted some of the central objects of stochastic geometry for more than 150 years. They are in general generated as convex hulls of a random set of points in the Euclidean space. The study of such models requires the use of ingredients coming from both convex geometry and probability theory. In the last decades, the study has been focused on their asymptotic properties and in particular expectation and variance estimates. In several joint works with Tomasz Schreiber and J. E. Yukich, we have investigated the scaling limit of several models (uniform model in the unit-ball, uniform model in a smooth convex body, Gaussian model) and have deduced from it limiting variances for several geometric characteristics including the number of k-dimensional faces and the volume. In this paper, we survey the most recent advances on these questions and we emphasize the particular cases of random polytopes in the unit-ball and Gaussian polytopes.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Raphaël Salem (UMR 6085), Université de Rouen, Mont-Saint-Aignan, France

    Pierre Calka

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  1. Pierre Calka
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Correspondence to Pierre Calka .

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Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Calka, P. (2015). Asymptotic Properties of Random Polytopes. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_22

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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