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Sharp concentration of random polytopes

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Geometric & Functional Analysis GAFA Aims and scope Submit manuscript

Abstract.

We prove that key functionals (such as the volume and the number of vertices) of a random polytope is strongly concentrated, using a martingale method. As applications, we derive new estimates for high moments and the speed of convergence of these functionals.

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Authors and Affiliations

  1. Department of Mathematics, UCSD, La Jolla, CA, 92093-0112, USA

    V. H. Vu

  2. Department of Mathematics, Rutgers, The State University of New Jersey, Rutgers, NJ, 08854, USA

    V. H. Vu

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  1. V. H. Vu
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Correspondence to V. H. Vu.

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Received: September 2004 Revision: November 2004 Accepted: November 2004

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Vu, V.H. Sharp concentration of random polytopes. GAFA, Geom. funct. anal. 15, 1284–1318 (2005). https://doi.org/10.1007/s00039-005-0541-8

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  • DOI: https://doi.org/10.1007/s00039-005-0541-8

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