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Entropy jumps in the presence of a spectral gap

Abstract : It is shown that if X is a random variable whose density satisfies a Poincare inequality, and Y is an independent copy of X, then the entropy of (X + Y)/root2 is greater than that of X by a fixed fraction of the entropy gap between X and the Gaussian of the same variance. The argument uses a new formula for the Fisher information of a marginal, which can be viewed as a local, reverse form of the Brunn-Minkowski inequality (in its functional form due to A. Prekopa and L Leindler).
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Submitted on : Tuesday, May 1, 2012 - 8:24:28 PM
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  • HAL Id : hal-00693115, version 1


K Ball, Franck Barthe, A Naor. Entropy jumps in the presence of a spectral gap. Duke Mathematical Journal, Duke University Press, 2003, 119 (1), pp.41--63. ⟨hal-00693115⟩



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