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Central limit theorems for random polytopes
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  • Published: 03 May 2005

Central limit theorems for random polytopes

  • Matthias Reitzner1 

Probability Theory and Related Fields volume 133, pages 483–507 (2005)Cite this article

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Abstract

Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances.

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Authors and Affiliations

  1. Inst. of Discrete Mathematics and Geometry, University of Technology Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Matthias Reitzner

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  1. Matthias Reitzner
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Correspondence to Matthias Reitzner.

Additional information

Research was supported in part by the European Network PHD, MCRN-511953.

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Cite this article

Reitzner, M. Central limit theorems for random polytopes. Probab. Theory Relat. Fields 133, 483–507 (2005). https://doi.org/10.1007/s00440-005-0441-8

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  • Received: 17 November 2004

  • Revised: 03 February 2005

  • Published: 03 May 2005

  • Issue Date: December 2005

  • DOI: https://doi.org/10.1007/s00440-005-0441-8

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Key words or phrases

  • Random polytopes
  • CLT
  • Approximation of convex bodies
  • Dependency graph
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