Approaching the Kannan-Lovasz-Simonovits and variance conjectures, volume 2131 of LNM, 2015. ,
Sur les inégalités de Sobolev logarithmiques, Panoramas et Synthèses. Société Mathématique de France, vol.10, 2000. ,
Intertwinings and generalized Brascamp-Lieb inequalities, Rev. Mat. Iberoam, vol.34, issue.3, pp.1021-1054, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01272885
Equivalent Harnack and gradient inequalities for pointwise curvature lower bound, Bull. Sci. Math, vol.138, pp.643-655, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01057529
Computation of sensitivities for the invariant measure of a parameter dependent diffusion, Stoch. Partial Differ. Equ. Anal. Comput, vol.6, issue.2, pp.125-183, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01192862
A simple proof of the Poincaré inequality for a large class of probability measures, Elec. Comm. in Prob, vol.13, pp.60-66, 2008. ,
Analysis and Geometry of Markov diffusion operators, Grundlehren der mathematischen Wissenchaften, vol.348, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00929960
On Harnack inequalities and optimal transportation, Ann. Scuola Norm-Sci, vol.14, pp.705-727, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00742654
Transference principles for log-sobolev and spectral-gap with applications to conservative spin systems, Comm. Math. Physics, vol.323, pp.575-625, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00960803
Isoperimetric and analytic inequalities for log-concave probability measures, Ann. Probab, vol.27, issue.4, pp.1903-1921, 1999. ,
Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations, J. Funct. Anal, vol.263, issue.8, pp.2430-2457, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00632941
Intertwining relations for one-dimensional diffusions and application to functional inequalities, Potential Analysis, vol.41, pp.1005-1031, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00812346
Spectral gap for spherically symmetric log-concave probability measures, and beyond, J. Funct. Anal, vol.270, issue.7, pp.2456-2482, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01009383
Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds, Available on Math. ArXiv, p.9186, 1906. ,
A pathwise approach of some classical inequalities, Potential. Anal, vol.20, pp.361-394, 2004. ,
Hypercontractivity for perturbed diffusion semigroups, Ann. Fac. Sciences Toulouse Math, vol.14, issue.6, pp.609-628, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00011201
Deviation bounds for additive functionals of Markov processes, ESAIM Probab. Stat, vol.12, pp.12-29, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00020035
Semi log-concave Markov diffusions, Séminaire de Probabilités XLVI, vol.2123, pp.231-292, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00805299
On the Poincaré constant of log-concave measures. To appear in Geometric Aspects of Functional Analysis: Israel Seminar (GAFA), 2019. ,
Poincaré inequalities and hitting times, Ann. Inst. Henri Poincaré. Prob. Stat, vol.49, issue.1, pp.95-118, 2013. ,
Eigenvalues of the drifted Laplacian on complete metric measure spaces, Comm. Contemp. Math, vol.17, 2017. ,
Stability in the Bakry-Emery theorem on R n, Arxiv preprint, 2018. ,
Rigidity and stability of Caffarelli's log-concave perturbation theorem, Nonlinear Anal, vol.154, pp.59-70, 2017. ,
More on the long time stability of Feynman-Kac semigroups, 2018. ,
Rigidity for the spectral gap on RCD(K, ?)-spaces. to appear in Amer, J. Math, 2018. ,
From concentration to logarithmic Sobolev and Poincaré inequalities, J. Funct. Anal, vol.260, pp.1491-1522, 2013. ,
Transportation-information inequalities for Markov processes, Probab. Theory Related Fields, vol.144, issue.3-4, pp.669-695, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00158258
Stochastic differential equations and diffusion processes, Kodansha, Ltd, vol.24, 1981. ,
Curvature, concentration and error estimates for Markov chain Monte Carlo, Ann. Probab, vol.38, issue.6, pp.2418-2442, 2010. ,
Isoperimetric problems for convex bodies and a localization lemma, Discrete Comput. Geom, vol.13, issue.3-4, pp.541-559, 1995. ,
Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes, Electron. J. Probab, vol.10, issue.3, pp.61-123, 2005. ,
Stochastic differential equations and stochastic flows of diffeomorphisms. InÉcole d'été de probabilités de Saint-Flour, XII-1982, Lecture Notes in Math, vol.1097, pp.143-303, 1984. ,
Duality on gradient estimates and Wasserstein controls, J. Funct. Anal, vol.258, issue.11, pp.3758-3774, 2010. ,
Eldan's stochastic localization and the KLS hyperplane conjecture: An improved lower bound for expansion, Proc. of IEEE FOCS, 2017. ,
Girsanov theory under a finite entropy condition. Séminaire de probabilités de Strasbourg, XLIV(Lecture Notes in Mathematics, pp.429-465, 2012. ,
Chernoff and Berry-Eessen inequalities for Markov processes, ESAIM Probability and Statistics, vol.5, pp.183-201, 2001. ,
Concentration inequalities for Euler schemes. In Monte Carlo and quasi-Monte Carlo methods, pp.355-371, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00452108
Integration by parts and time reversal for diffusion processes, Ann. Probab, vol.17, issue.1, pp.208-238, 1989. ,
On the role of convexity in isoperimetry, spectral-gap and concentration, Invent. math, vol.177, pp.1-43, 2009. ,
Isoperimetric and concentration inequalities: Equivalence under curvature lower bound, Duke Math. J, vol.154, issue.2, pp.207-239, 2010. ,
Equality in the logarithmic Sobolev inequality, Manuscripta Math, 2019. ,
Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality, J. Funct. Anal, vol.173, pp.361-400, 2000. ,
Weak Poincaré inequalities and L 2 -convergence rates of Markov semigroups, J. Funct. Anal, vol.185, issue.2, pp.564-603, 2001. ,
Improved spectral gap bounds on positively curved manifolds, Available on Math. ArXiv. 1105.6080, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00596725
Transport inequalities, gradient estimates, entropy and Ricci curvature, Comm. Pure Appl. Math, vol.68, pp.923-940, 2005. ,
, Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. Probab. Theory Related Fields, vol.109, pp.417-424, 1997.
Functional inequalities, Markov processes and Spectral theory, 2005. ,
A deviation inequality for non-reversible Markov process, Ann. Inst. Henri Poincaré. Prob. Stat, vol.36, issue.4, pp.435-445, 2000. ,
, CNRS UMR, vol.5219
, E-mail address: patrick.cattiaux@math.univ-toulouse.fr
, CNRS UMR, vol.5219
, E-mail address: max.fathi@math.univ-toulouse.fr
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