Approaching the Kannan-Lovasz-Simonovits and variance conjectures, volume 2131 of LNM, 2015. ,
A simple proof of the Poincaré inequality for a large class of probability measures, Elec. Comm. in Prob, vol.13, pp.60-66, 2008. ,
Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré, J. Funct. Anal, vol.254, pp.727-759, 2008. ,
Analysis and Geometry of Markov diffusion operators, Grundlehren der mathematischen Wissenchaften, vol.348, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00929960
Entropy jumps in the presence of a spectral gap, Duke Math. J, vol.119, pp.41-63, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00693115
Concentration for independent random variables with heavy tails, AMRX, issue.2, pp.39-60, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00004959
Invariances in variance estimates, Proc. Lond. Math. Soc, vol.106, issue.1, pp.33-64, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00960795
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
Concentration of measure, 2009. ,
Isoperimetric and analytic inequalities for log-concave probability measures, Ann. Prob, vol.27, issue.4, pp.1903-1921, 1999. ,
Spectral gap and concentration for some spherically symmetric probability measures, Geometric aspects of functional analysis, vol.1807, pp.37-43, 2000. ,
Proximity of probability distributions in terms of Fourier-Stieltjes transforms, Russian Math. Surveys, vol.71, issue.6, pp.1021-1079, 2016. ,
Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pu. Appli, vol.80, issue.7, pp.669-696, 2001. ,
Isoperimetric constants for product probability measures, Ann. Probab, vol.25, issue.1, pp.184-205, 1997. ,
Poincaré's inequalities and Talagrand's concentration phenomenon for the exponential distribution, vol.107, pp.383-400, 1997. ,
On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Funct. Anal, vol.22, pp.366-389, 1976. ,
Geometry of isotropic convex bodies, Math. Surveys and Monographs, vol.196, 2014. ,
Functional inequalities for heavy tails distributions and applications to isoperimetry, Electronic J. of Proba, vol.15, pp.346-385, 2010. ,
Semi log-concave Markov diffusions. Séminaire de Probabilités XLVI, Lect. Notes Math, pp.231-292, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00805299
Hitting times, functional inequalities, Lyapunov conditions and uniform ergodicity, J. Funct. Anal, vol.272, issue.6, pp.2361-2391, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01303903
Poincaré inequality and the L p convergence of semi-groups, Elec. Comm. in Prob, vol.15, pp.270-280, 2010. ,
Poincaré inequalities and hitting times, Ann. Inst. Henri Poincaré. Prob. Stat, vol.49, issue.1, pp.95-118, 2013. ,
Transport proofs of weighted Poincaré inequalities for log-concave distributions, Bernoulli, vol.23, issue.1, pp.134-158, 2017. ,
Distances of probability measures and random variables, Ann. Math. Statist, vol.39, pp.1563-1572, 1968. ,
, Real Analysis and Probability, 2002.
Reflection coupling and Wasserstein contractivity without convexity, C. R. Acad. Sci. Paris, Ser. I, vol.349, pp.1101-1104, 2011. ,
Reflection couplings and contraction rates for diffusions, vol.166, pp.851-886, 2016. ,
Concentration inequalities for s-concave measures of dilations of Borel sets and applications, Electronic J. of Proba, vol.14, issue.71, pp.2068-2090, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00693040
Interpolating thin shell and sharp large deviation estimates for isotropic log-concave measures, Geom. Funct. Anal, vol.21, pp.1043-1068, 2011. ,
Isoperimetry for spherically symmetric log-concave probability measures, Rev. Mat. Iberoamericana, vol.27, issue.1, pp.93-122, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00358888
Isoperimetric problems for convex bodies and a localization lemma, Discrete Comput. Geom, vol.13, issue.3-4, pp.541-559, 1995. ,
A Berry-Esseen type inequality for convex bodies with an unconditional basis, vol.145, pp.1-33, 2009. ,
Poincaré inequalities and moment maps, Ann. Fac. Sci. Toulouse Math, vol.22, issue.1, pp.1-41, 2013. ,
Concentration of measures supported on the cube, Israel J. Math, vol.203, issue.1, pp.59-80, 2014. ,
On diffusion semigroups preserving the log-concavity, J. Funct. Anal, vol.186, issue.1, pp.196-205, 2001. ,
Order statistics and concentration of L r norms for log-concave vectors, J. Funct. Anal, vol.261, pp.681-696, 2011. ,
Spectral gap, logarithmic Sobolev constant, and geometric bounds, Surveys in differential geometry., volume IX, pp.219-240, 2004. ,
From concentration to isoperimetry: semigroup proofs, Contemp. Math, vol.505, pp.155-166, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00993118
On the equivalence of modes of convergence for log-concave measures, Geometric aspects of functional analysis, vol.2116, pp.385-394, 2014. ,
On the role of convexity in isoperimetry, spectral-gap and concentration, Invent. math, vol.177, pp.1-43, 2009. ,
Isoperimetric bounds on convex manifolds, Concentration, Functional inequality and Isoperimetry, vol.545, pp.195-208, 2011. ,
DOI : 10.1090/conm/545/10772
URL : http://arxiv.org/pdf/1004.0485.pdf
The methods of distances in the theory of probability and statistics, 2013. ,
Weak Poincaré inequalities and L 2-convergence rates of Markov semigroups, J. Funct. Anal, vol.185, issue.2, pp.564-603, 2001. ,
Log-concavity and strong log-concavity: a review, Statistics Surveys, vol.8, pp.45-114, 2014. ,
DOI : 10.1214/14-ss107
URL : https://doi.org/10.1214/14-ss107
Concentration et inégalité de Poincaré, 2001. ,
Logarithmic Sobolev inequalities for mollified compactly supported measures, J. Funct. Anal, vol.265, pp.1064-1083, 2013. ,
DOI : 10.1016/j.jfa.2013.05.029
URL : http://arxiv.org/pdf/1411.1688
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