A. Barron, The Strong Ergodic Theorem for Densities: Generalized Shannon-McMillan-Breiman Theorem, The Annals of Probability, vol.13, issue.4, pp.1292-1303, 1985.
DOI : 10.1214/aop/1176992813

S. Bobkov, M. Fradelizi, J. Li, and M. Madiman, When can one invert Hölder's inequality? (and why one may want to), 2015.

S. Bobkov and M. Madiman, Concentration of the information in data with log-concave distributions, The Annals of Probability, vol.39, issue.4, pp.1528-1543, 2011.
DOI : 10.1214/10-AOP592

C. Borell, Complements of Lyapunov's inequality, Mathematische Annalen, vol.21, issue.4, pp.323-331, 1973.
DOI : 10.1007/BF01362702

J. Bourgain, On High Dimensional Maximal Functions Associated to Convex Bodies, American Journal of Mathematics, vol.108, issue.6, pp.1467-1476, 1986.
DOI : 10.2307/2374532

L. Breiman, The Individual Ergodic Theorem of Information Theory, The Annals of Mathematical Statistics, vol.28, issue.3, pp.809-811, 1957.
DOI : 10.1214/aoms/1177706899

T. M. Cover and S. Pombra, Gaussian feedback capacity, IEEE Transactions on Information Theory, vol.35, issue.1, pp.37-43, 1989.
DOI : 10.1109/18.42174

M. Fradelizi, O. Guédon, and A. Pajor, Thin-shell concentration for convex measures, Studia Mathematica, vol.223, issue.2, pp.123-148, 2014.
DOI : 10.4064/sm223-2-2

URL : https://hal.archives-ouvertes.fr/hal-01073062

M. Fradelizi, M. Madiman, and L. Wang, Optimal Concentration of Information Content for Log-Concave Densities, High Dimensional Probability VII, 2015.
DOI : 10.1007/BF00635964

O. Guédon, P. Nayar, and T. Tkocz, Concentration inequalities and geometry of convex bodies, " in Analytical and Probabilistic Methods in the Geometry of Convex Bodies, ser. IM PAN Lecture Notes, Warsaw: Polish Acad. Sci, vol.2, pp.9-86, 2014.

M. Madiman, L. Wang, and S. Bobkov, Some applications of the nonasymptotic equipartition property of log-concave distributions, 2016.

B. Mcmillan, The Basic Theorems of Information Theory, The Annals of Mathematical Statistics, vol.24, issue.2, pp.196-219, 1953.
DOI : 10.1214/aoms/1177729028

V. H. Nguyen, Dimensional variance inequalities of Brascamp???Lieb type and a local approach to dimensional Pr??kopa??s theorem, Journal of Functional Analysis, vol.266, issue.2, pp.931-955, 2014.
DOI : 10.1016/j.jfa.2013.11.003

S. Orey, On the Shannon-Perez-Moy theorem, Particle systems, random media and large deviations, 1984.
DOI : 10.1090/conm/041/814721

C. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948.
DOI : 10.1002/j.1538-7305.1948.tb01338.x