Gradient flows in metric spaces and in the space of probability measures, Lectures in Math. ETH Zürich. Birkhäuser, 2008. ,
Intertwinings and generalized Brascamp-Lieb Inequalities ,
URL : https://hal.archives-ouvertes.fr/hal-01272885
Dimension dependent hypercontractivity for Gaussian kernels, Probability Theory and Related Fields, vol.118, issue.3, pp.845-874, 2012. ,
DOI : 10.1007/s00440-011-0387-y
URL : https://hal.archives-ouvertes.fr/hal-00465879
Analysis and geometry of Markov diffusion operators, Grund. Math. Wiss. Springer, vol.348 ,
DOI : 10.1007/978-3-319-00227-9
URL : https://hal.archives-ouvertes.fr/hal-00929960
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
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
Bounds on the deficit in the logarithmic Sobolev inequality, Journal of Functional Analysis, vol.267, issue.11, pp.4110-4138, 2014. ,
DOI : 10.1016/j.jfa.2014.09.016
URL : https://hal.archives-ouvertes.fr/hal-01053507
From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities, Geometric and Functional Analysis, vol.10, issue.5, pp.1028-1052, 2000. ,
DOI : 10.1007/PL00001645
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.3360
From Brunn???Minkowski to sharp Sobolev inequalities, Annali di Matematica Pura ed Applicata, vol.110, issue.3, pp.369-384, 2008. ,
DOI : 10.1007/s10231-007-0047-0
URL : https://hal.archives-ouvertes.fr/hal-00634578
Weighted Poincar??-type inequalities for Cauchy and other convex measures, The Annals of Probability, vol.37, issue.2, pp.403-427, 2009. ,
DOI : 10.1214/08-AOP407
URL : http://arxiv.org/abs/0906.1651
Convergence to equilibrium in Wasserstein distance for Fokker???Planck equations, Journal of Functional Analysis, vol.263, issue.8, pp.2430-2457, 2012. ,
DOI : 10.1016/j.jfa.2012.07.007
URL : https://hal.archives-ouvertes.fr/hal-00632941
Dimensional contraction via Markov transportation distance, Journal of the London Mathematical Society, vol.135, issue.1, pp.309-332, 2014. ,
DOI : 10.1112/jlms/jdu027
URL : https://hal.archives-ouvertes.fr/hal-00808717
Equivalence between dimensional contractions in Wasserstein distance and curvature-dimension condition ,
URL : https://hal.archives-ouvertes.fr/hal-01220776
Superadditivity of Fisher's information and logarithmic Sobolev inequalities, Journal of Functional Analysis, vol.101, issue.1, pp.194-211, 1991. ,
DOI : 10.1016/0022-1236(91)90155-X
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
Transport inequalities for log-concave measures, quantitative forms and applications ,
DOI : 10.4153/cjm-2016-046-3
URL : http://arxiv.org/abs/1504.06147
Lecture notes on gradient flows and optimal transport. Optimal transportation, Soc. Lecture Note Ser, vol.413, pp.100-144, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00519401
The optimal Euclidean L p -Sobolev logarithmic inequality, J. Funct. Anal, vol.197, issue.1, pp.151-161, 2003. ,
A two-sided estimate for the Gaussian noise stability deficit, Inventiones mathematicae, vol.6, issue.1, pp.561-624, 2015. ,
DOI : 10.1007/s00222-014-0556-6
On the equivalence of the entropic curvature-dimension condition and Bochner???s inequality on metric measure spaces, Inventiones mathematicae, vol.91, issue.3, pp.993-1071, 2015. ,
DOI : 10.1007/s00222-014-0563-7
Quantitative logarithmic Sobolev inequalities and stability estimates, Discrete and Continuous Dynamical Systems, vol.36, issue.12, pp.6835-6853, 2016. ,
DOI : 10.3934/dcds.2016097
URL : http://arxiv.org/abs/1410.6922
A Sharp Stability Result for the Relative Isoperimetric Inequality Inside Convex Cones, Journal of Geometric Analysis, vol.23, issue.4, pp.938-969, 2013. ,
DOI : 10.1007/s12220-011-9270-4
Quantitative stability for the Brunn-Minkowski inequality ,
A mass transportation approach to quantitative isoperimetric inequalities, Inventiones mathematicae, vol.34, issue.4, pp.167-211, 2010. ,
DOI : 10.1007/s00222-010-0261-z
Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation, Advances in Mathematics, vol.242, pp.80-101, 2013. ,
DOI : 10.1016/j.aim.2013.04.007
Reinforcement of an inequality due to Brascamp and Lieb, Journal of Functional Analysis, vol.254, issue.2, pp.267-300, 2008. ,
DOI : 10.1016/j.jfa.2007.07.019
A Quantitative Log-Sobolev Inequality for a Two Parameter Family of Functions, International Mathematics Research Notices, vol.20, pp.5563-5580, 2014. ,
DOI : 10.1093/imrn/rnt138
Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces, ESAIM: Control, Optimisation and Calculus of Variations, vol.15, issue.3, pp.712-740, 2009. ,
DOI : 10.1051/cocv:2008044
A Convexity Principle for Interacting Gases, Advances in Mathematics, vol.128, issue.1, pp.153-179, 1997. ,
DOI : 10.1006/aima.1997.1634
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
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
Transportation cost for Gaussian and other product measures, Geometric and Functional Analysis, vol.27, issue.3, pp.587-600, 1996. ,
DOI : 10.1007/BF02249265
Topics in Optimal transportation, volume 58 of Grad. studies in math, 2003. ,
Optimal transport, Old and new, 2009. ,