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Entropy jumps for isotropic log-concave random vectors and spectral gap

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Ball, Keith M. and Nguyen, Van Hoang (2012) Entropy jumps for isotropic log-concave random vectors and spectral gap. Studia Mathematica, Volume 213 (Number 1). pp. 81-96. doi:10.4064/sm213-1-6 ISSN 0039-3223.

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Official URL: http://dx.doi.org/10.4064/sm213-1-6

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Abstract

We prove a quantitative dimension-free bound in the Shannon{Stam en- tropy inequality for the convolution of two log-concave distributions in dimension d in terms of the spectral gap of the density. The method relies on the analysis of the Fisher information production, which is the second derivative of the entropy along the (normalized) heat semigroup. We also discuss consequences of our result in the study of the isotropic constant of log-concave distributions (slicing problem).

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: Studia Mathematica
Publisher: Polska Akademia Nauk
ISSN: 0039-3223
Official Date: 2012
Dates:
DateEvent
2012Published
Volume: Volume 213
Number: Number 1
Page Range: pp. 81-96
DOI: 10.4064/sm213-1-6
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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