Publications

Conditional principles for random weighted measures. ESAIM PS, 9 (2005) 283-306.

Integral criteria for transportation-cost inequalities. Electronic Communications in Probability 11 (2006)  64-77.

Deviations bounds and conditional principles for thin sets, with P. Cattiaux. Stochastic Processes and their Applications, 117 (2007)  221-250.

A large deviation approach to some transportation cost inequalities, with C. Léonard. Probability Theory and Related Fields 139 (2007), no. 1-2, 235-283.

Characterization of Talagrand's like transportation-cost inequalities on the real line. Journal of Functional Analysis 250 (2007), no. 2, 400-425.

A characterization of dimension free concentration in terms of transport inequalities. Annals of Probability 37 (2009), no. 6, 2480-2498.

Functional inequalities for heavy tailed distributions and application to isoperimetry, with P. Cattiaux, A. Guillin and C. Roberto. Electronic Journal of Probability, 15 (2010), 346-385.

Poincaré inequalities and dimension free concentration of measure. Annales de l'Institut Henri Poincaré - Probabilités et Statistiques, 46 (2010), no. 3,  708-739.

Isoperimetry for product of heavy tails distributions, with C. Roberto and P-M Samson. Progress in analysis and its applications,  World Sci. Publ., Hackensack (2010), 470-478.

Transport inequalities. A survey, with C. Léonard. Markov Processes and Related Fields 16 (2010), 635-736.

From concentration to logarithmic Sobolev and Poincaré  inequalities, with C. Roberto and P-M. Samson. Journal of Functional Analysis 260 (2011), no. 5, 1491-1522.

A new characterization of Talagrand's transport-entropy inequalities and applications, with C. Roberto and P-M. Samson. Annals of Probability 39 (2011), no. 3, 857-880.

Transport-entropy inequalities on the line,  Electronic Journal of Probability, 17 (2012), no. 49, 1-18.

The logarithmic Sobolev constant of the lamplighter, with C. Roberto and P-M. Samson. Journal of Mathematical Analysis and Applications 399 (2013), no. 2, 576-585.

Characterization of Talagrand's transport-entropy inequalities on metric spaces, with C. Roberto and P-M Samson, Annals of Probability 41 (2013), no. 5, 3112-3139.

Hamilton-Jacobi equations on metric spaces and transport-entropy inequalities, with C. Roberto and P-M Samson, Revista Matematica Iberoamericana 30 (2014), no. 1, 133-163.

Displacement convexity of entropy and related inequalities on graphs, with C. Roberto, P-M Samson and P. Tetali, Probability Theory and Related Fields 160 (2014) no. 1-2, 47- 94.

First order global asymptotics for confined particles with singular pair repulsion, with D. Chafaï and P-A Zitt, Annals of Applied Probability 24 (2014) no. 6, 2371-2413.

Bounds on the deficit in the logarithmic Sobolev inequality, with S. Bobkov, C. Roberto and P-M Samson, Journal of Functional Analysis 267 (2014), no. 11, 4110-4138.

From dimension free concentration to Poincaré inequality, with C. Roberto and P-M Samson, Calculus of Variations and Partial Differential Equations 52 (2015), no. 3-4, 899-925.

Transport proofs of weighted Poincaré inequalities for log concave distributions, with D. Cordero-Erausquin, Bernoulli (2017) no. 1, 134-158.

A variational approach to some transport inequalities, with J. Fontbona and J-F. Jabir, Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 53 (2017), no. 4, 1719–1746.

Kantorovich duality for general costs and applications, with C. Roberto, P-M Samson and P-Tetali,  Journal of Functional Analysis 273 (2017), no. 11, 3327–3405.

Deviation inequalities for convex functions motivated by the Talagrand conjecture, with M. Madiman, C. Roberto and P-M Samson, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 457 (2017), Veroyatnostʹ i Statistika. 25, 168–182.

Functional inequalities for Gaussian convolutions of compactly supported measures: explicit bounds and dimension dependence, with J-B. Bardet, F. Malrieu and P-A Zitt, Bernoulli 24 (2018), no. 1, 333-353.

Characterization of a class of weak transport inequalities on the line, avec C. Roberto, P-M Samson, Y. Shu and P. Tetali, Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 54 (2018), no. 3, 1667–1693.

On a mixture of Brenier and Strassen theorems, with N. Juillet, Proceedings of the London Mathematical Society 120 (2020), no. 3, 434-463.

Multiple sets exponential concentration and higher order eigenvalues, with R. Herry, Potential Analysis 52 (2020), no. 2, 203–221.

A proof of the Caffarelli contraction theorem via entropic regularization, with M. Fathi and M. Prodhomme, Calculus of Variations and Partial Differential Equations (2020), no. 3, Paper No. 96, 18 pp.

Transport proofs of some discrete variants of the Prekopa-Leindler inequality, with C. Roberto, P-M Samson, P. Tetali, Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze, No. 3, 1207-1232 (2021).

Transport inequalities for random point measures, with R. Herry and G. Peccati. Journal of Functional Analysis 281 (2021), No. 9, 45 p. 

The deficit in the Gaussian Log-Sobolev inequality and inverse Santalo inequalities. International Mathematics Research Notices, Volume 2022, Issue 17, August 2022, Pages 12940–12983 (2022). Slides (exposé du groupe de travail CTOP)

Log-Hessian formula and the Talagrand conjecture, with X.-M. Li, M. Madiman, C. Roberto and P-M Samson. Potential Analysis 58 (2023), no. 1, 123–158.

Transport proofs of some functional inverse Santaló inequalities, with M. Fradelizi and S. Zugmeyer. In Radosław Adamczak, Nathael Gozlan, Karim Lounici, and Mokshay Madiman, editors, High Dimensional Probability IX, pages 123–142, Cham, 2023. Springer International Publishing.

Generalized Wasserstein barycenters between probability measures living on different subspaces, with J. Delon and A. Saint-Dizier. Annals of Applied Probability (2023), Vol. 33, No. 6A, 4395-4423.

Weak Optimal Transport with unnormalized kernels, with P. Choné and F. Kramarz. SIAM Journal on Mathematical Analysis 55, No. 6, 6039-6092 (2023).
Note. In the published version of this paper, the proof of Theorem 3.2 contained an error, which has been fixed in the version available on HAL or ArXiv.

Transport-entropy and functional forms of Blaschke-Santaló inequalities, with M. Fradelizi, S. Sadovsky and S. Zugmeyer. Accepted in Revista Matemática Iberoamericana (2023).

Some obstructions to contraction theorems on the half-sphere, with M. Fathi, M. Fradelizi and S. Zugmeyer (2024).

Duality and heat flow, with D. Cordero-Erausquin, S. Nakamura and H. Tsuji (2024)