Gentil, I. Dimension dependent hypercontractivity for Gaussian kernels, Probab. Theory Related Fields, vol.154, pp.3-4, 2012. ,
Diffusions hypercontractives. Seminaire de probabilites, XIX, Lecture Notes in Math, vol.84, pp.177-206, 1123. ,
A logarithmic Sobolev form of the Li-Yau parabolic inequality, Revista Matem??tica Iberoamericana, vol.22, issue.2, pp.683-702, 2006. ,
DOI : 10.4171/RMI/470
URL : https://hal.archives-ouvertes.fr/hal-00353946
Mass Transport and Variants of the Logarithmic Sobolev Inequality, Journal of Geometric Analysis, vol.22, issue.1, pp.921-979, 2008. ,
DOI : 10.1007/s12220-008-9039-6
URL : https://hal.archives-ouvertes.fr/hal-00634530
The convolution inequality for entropy powers, IEEE Transactions on Information Theory, vol.11, issue.2, pp.267-271, 1965. ,
DOI : 10.1109/TIT.1965.1053768
Hypercontractivity of Hamilton???Jacobi equations, Journal de Math??matiques Pures et Appliqu??es, vol.80, issue.7, pp.669-696, 2001. ,
DOI : 10.1016/S0021-7824(01)01208-9
Exponential Integrability and Transportation Cost Related to Logarithmic Sobolev Inequalities, Journal of Functional Analysis, vol.163, issue.1, pp.1-28, 1999. ,
DOI : 10.1006/jfan.1998.3326
URL : http://doi.org/10.1006/jfan.1998.3326
Isoperimetric constants for product probability measures Superadditivity of Fisher's information and logarithmic Sobolev inequalities, Ann. Probab. J. Funct. Anal, vol.25, issue.101 1, pp.184-205, 1991. ,
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation. Duke Math, J, vol.162, issue.3, pp.579-625, 2013. ,
On the isoperimetric deficit in Gauss space, American Journal of Mathematics, vol.133, issue.1, pp.131-186, 2011. ,
DOI : 10.1353/ajm.2011.0005
Some Applications of Mass Transport to Gaussian-Type Inequalities, Archive for Rational Mechanics and Analysis, vol.161, issue.3, pp.257-269, 2002. ,
DOI : 10.1007/s002050100185
URL : https://hal.archives-ouvertes.fr/hal-00693655
Information theoretic inequalities, IEEE Transactions on Information Theory, vol.37, issue.6, pp.1501-1518, 1991. ,
DOI : 10.1109/18.104312
Improved interpolation inequalities, relative entropy and fast diffusion equations. To appear in Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2013). [E] Eldan, R. A two-sided estimate for the Gaussian noise stability deficit, p.13072781, 2013. ,
DOI : 10.1016/j.anihpc.2012.12.004
URL : https://hal.archives-ouvertes.fr/hal-00634852
On the equivalence of the entropic curvature-dimension condition and Bochner???s inequality on metric measure spaces, Inventiones mathematicae, vol.91, issue.3, p.13034382, 2013. ,
DOI : 10.1007/s00222-014-0563-7
A refined Brunn???Minkowski inequality for convex sets, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.6, pp.2511-2519, 2009. ,
DOI : 10.1016/j.anihpc.2009.07.004
The sharp quantitative Sobolev inequality for functions of bounded variation, Journal of Functional Analysis, vol.244, issue.1, p.315341, 2007. ,
DOI : 10.1016/j.jfa.2006.10.015
Transport inequalities -A survey, Markov Processes and Related Fields, vol.16, pp.635-736, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00515419
Logarithmic Sobolev Inequalities, American Journal of Mathematics, vol.97, issue.4, pp.1061-1083, 1975. ,
DOI : 10.2307/2373688
A quantitative log-Sobolev inequality for a two parameter family of functions. To appear in Int, Math. Res. Not, 2013. ,
Concentration of measure and logarithmic Sobolev inequalities, Lecture Notes in Math, vol.27, issue.12, pp.120-216, 1999. ,
DOI : 10.1007/s004400050137
The concentration of measure phenomenon, Math. Surveys and monographs, vol.89, 2001. ,
DOI : 10.1090/surv/089
On a certain converse of Hölder's inequality II, stochastic programming, Acta Sci. Math. Szeged, vol.33, pp.217-223, 1972. ,
Proof of an entropy conjecture of Wehrl, Communications in Mathematical Physics, vol.31, issue.1, pp.35-41, 1978. ,
DOI : 10.1007/BF01940328
Robust dimension free isoperimetry in Gaussian space Preprint (2012) To appear in Information and information stability of random variables and processes, 1964. ,
Logarithmic concave measures with applications to stochastic programming, Acta Sci. Math. Szeged, vol.32, pp.301-316, 1971. ,
On logarithmic concave measures and functions, Acta Sci. Math. Szeged, vol.34, pp.335-343, 1973. ,
Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality, Journal of Functional Analysis, vol.173, issue.2, pp.361-400, 2000. ,
DOI : 10.1006/jfan.1999.3557
Concentration of Measure Inequalities in Information Theory, Communications, and Coding, issues 1 and 2, pp.1-246, 2013. ,
DOI : 10.1561/0100000064
Remark on Stability of Brunn???Minkowski and Isoperimetric Inequalities for Convex Bodies, Lecture Notes in Mathematics, vol.2050, pp.381-391, 2012. ,
DOI : 10.1007/978-3-642-29849-3_24
Some inequalities satisfied by the quantities of information of Fisher and Shannon Transportation cost for Gaussian and other product measures, Information and Control Geom. Funct. Anal, vol.2, issue.6, pp.101-112, 1959. ,
Optimal transport: Old and new, 2009. ,
DOI : 10.1007/978-3-540-71050-9
Generalized transportation-cost inequalities and applications. Potential Anal, pp.321-334, 2008. ,
A Simple Transportation-Information Inequality, with Applications to HWI Inequalities and Predictive Density Estimation, 2011. ,