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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
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Official URL: http://dx.doi.org/10.4064/sm213-1-6
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 > Mathematics | ||||
| Journal or Publication Title: | Studia Mathematica | ||||
| Publisher: | Polska Akademia Nauk | ||||
| ISSN: | 0039-3223 | ||||
| Official Date: | 2012 | ||||
| Dates: |
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| 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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