Original Paper

Geometric & Functional Analysis GAFA

, Volume 15, Issue 6, pp 1284-1318

First online:

Sharp concentration of random polytopes

  • V. H. VuAffiliated withDepartment of Mathematics, UCSDDepartment of Mathematics, Rutgers, The State University of New Jersey Email author 

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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.