[Comportement dimensionnel de l'entropie et de l'information]
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.
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@article{CRMATH_2011__349_3-4_201_0,
author = {Bobkov, Sergey and Madiman, Mokshay},
title = {Dimensional behaviour of entropy and information},
journal = {Comptes Rendus. Math\'ematique},
pages = {201--204},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2011.01.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.01.008/}
}
TY - JOUR AU - Bobkov, Sergey AU - Madiman, Mokshay TI - Dimensional behaviour of entropy and information JO - Comptes Rendus. Mathématique PY - 2011 SP - 201 EP - 204 VL - 349 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.01.008/ DO - 10.1016/j.crma.2011.01.008 LA - en ID - CRMATH_2011__349_3-4_201_0 ER -
%0 Journal Article %A Bobkov, Sergey %A Madiman, Mokshay %T Dimensional behaviour of entropy and information %J Comptes Rendus. Mathématique %D 2011 %P 201-204 %V 349 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.01.008/ %R 10.1016/j.crma.2011.01.008 %G en %F CRMATH_2011__349_3-4_201_0
Bobkov, Sergey; Madiman, Mokshay. Dimensional behaviour of entropy and information. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 201-204. doi : 10.1016/j.crma.2011.01.008. http://www.numdam.org/articles/10.1016/j.crma.2011.01.008/
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