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