Dimensional behaviour of entropy and information

Sergey Bobkov; Mokshay Madiman

doi:10.1016/j.crma.2011.01.008

Functional Analysis/Probability Theory

Dimensional behaviour of entropy and information
[Comportement dimensionnel de l'entropie et de l'information]

Présenté par : Gilles Pisier

Sergey Bobkov ¹ ; Mokshay Madiman ²

¹ School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
² Department of Statistics, Yale University, New Haven, CT 06511, USA

Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 201-204.

Résumé
Abstract

Nous développons un point de vue de théorie de l'information sur certains problèmes de géométrie des convexes, fournissant par exemple une nouvelle propriété d'équipartition des mesures de probabilités log-concaves, une inégalité de comparaison gaussienne de l'entropie de mesures log-concaves, une formulation entropique de la conjecture de l'hyperplan, et une nouvelle inégalité inverse concernant l'entropie exponentielle pour des mesures log-concaves, analogue à l'inégalité inverse Brunn–Minkowski due à V. Milman.

We develop an information-theoretic perspective on some questions in convex geometry, providing for instance a new equipartition property for log-concave probability measures, some Gaussian comparison results for log-concave measures, an entropic formulation of the hyperplane conjecture, and a new reverse entropy power inequality for log-concave measures analogous to V. Milman's reverse Brunn–Minkowski inequality.

Reçu le : 2010-10-13
Accepté le : 2011-01-05
Publié le : 2011-01-22

DOI : 10.1016/j.crma.2011.01.008

Affiliations des auteurs :

Sergey Bobkov ¹ ; Mokshay Madiman ²

¹ School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
² Department of Statistics, Yale University, New Haven, CT 06511, USA

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     title = {Dimensional behaviour of entropy and information},
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     language = {en},
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Sergey Bobkov; Mokshay Madiman. Dimensional behaviour of entropy and information. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 201-204. doi : 10.1016/j.crma.2011.01.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.008/

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