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.
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.
Accepted:
Published online:
Sergey Bobkov 1; Mokshay Madiman 2
@article{CRMATH_2011__349_3-4_201_0,
author = {Sergey Bobkov and Mokshay Madiman},
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},
}
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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