On the Geometry of Log-Concave Probability Measures with Bounded Log-Sobolev Constant

Chapter
Part of the Fields Institute Communications book series (FIC, volume 68)

Abstract

Let \(\mathcal{L}S_{lc}(\kappa )\) denote the class of log-concave probability measures μ on \({\mathbb{R}}^{n}\) which satisfy the logarithmic Sobolev inequality with a given constant κ > 0. We discuss \(\mathcal{L}S_{lc}(\kappa )\) from a geometric point of view and we focus on related open questions.

Key words

Log-Sobolev inequality (τ)-property ψ2-measures 

Notes

Acknowledgements

We would like to thank A. Giannopoulos for many interesting discussions. We also thank E. Milman and R. Latała for useful references on the subject of this work.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AthensAthensGreece

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