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SPECTRAL GAP FOR SOME INVARIANT LOG-CONCAVE PROBABILITY MEASURES

Part of: Inequalities Distribution theory - Probability Classical measure theory

Published online by Cambridge University Press:  22 November 2010

Nolwen Huet
Nolwen Huet*
Affiliation:
Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université de Toulouse, 31062 Toulouse, France (email: nolwen.huet@math.univ-toulouse.fr)
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Abstract

We show that the conjecture of Kannan, Lovász, and Simonovits on isoperimetric properties of convex bodies and log-concave measures is true for log-concave measures of the form ρ(∣x∣B) dx on ℝn and ρ(t,∣x∣B) dx on ℝ1+n, where ∣x∣B is the norm associated to any convex body B already satisfying the conjecture. In particular, the conjecture holds for convex bodies of revolution.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory 26D10: Inequalities involving derivatives and differential and integral operators 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Mathematika , Volume 57 , Issue 1 , January 2011 , pp. 51 - 62
Copyright
Copyright © University College London 2011

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