Central limit theorems for random polytopes in a smooth convex set

• Autores: Van H. Vu
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 1, 2006, págs. 221-243
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.11.011
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• Resumen

  • Let K be a smooth convex set with volume one in . Choose n random points in K independently according to the uniform distribution. The convex hull of these points, denoted by Kn, is called a random polytope. We prove that several key functionals of Kn satisfy the central limit theorem as n tends to infinity.