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

  • P. Stavrakakis
  • P. Valettas
Part of the Fields Institute Communications book series (FIC, volume 68)


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 



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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