The Geometry of Random {-1,1}-Polytopes

  • Authors:

  • S. Mendelson;A. Pajor_aff1n2;M. Rudelson

  • Affiliations:

  • Centre for Mathematics and its Applications, Institute of Advanced Studies, The Australian National University, Canberra, ACT 0200, Australia;Centre for Math. and its Apps., Inst. of Adv. Studies, The Aus. Natl. Univ, Canberra, ACT 0200, Australia and Laboratoire d’Analyse et Mathematiques Appliquees, Universite de Marne-la-Valle ...;Department of Mathematics, University of Missouri, Columbia, MO 65211, USA

  • Venue:
  • Discrete & Computational Geometry
  • Year:
  • 2005

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Abstract

Random {-1,1}-polytopes demonstrate extremal behavior with respect to many geometric characteristics. We illustrate this by showing that the combinatorial dimension, entropy and Gelfand numbers of these polytopes are extremal at every scale of their arguments.