Geometric & Functional Analysis GAFA

, Volume 15, Issue 6, pp 1284–1318

Sharp concentration of random polytopes

Original Paper

DOI: 10.1007/s00039-005-0541-8

Cite this article as:
Vu, V.H. GAFA, Geom. funct. anal. (2005) 15: 1284. doi:10.1007/s00039-005-0541-8


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.

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of MathematicsUCSDLa JollaUSA
  2. 2.Department of MathematicsRutgers, The State University of New JerseyRutgersUSA