Publications

Preprints:

Melbourne, Nayar, Roberto Minimum entropy of a log-concave variable for fixed variance . Preprint (2023).
Bobkov, Roberto Entropic isoperimetric inequalities for generalized Fischer information . Preprint to appear in a Special Issue on Analysis and PDE dedicated to Professor Vladimir Maz'ya on the occasion of his 85th birthday, Journal "Pure and Applied Functional Analysis".
Barki, Bobkov, bou Dagher, Roberto Exponential inequalities in probability spaces revisited . Preprint (2023).

List of publications:

Bobkov, Roberto Entropic isoperimetric inequalities . Progr. Probab., 80 Birkhäuser/Springer, Cham, (2023) 97–121.
Melbourne, Roberto Transport-majorization to analytic and geometric inequalities. Journal of Functional Analysis 284 (2023), no. 1, Paper No. 109717, 36 pp.
Madiman, Melbourne, Roberto Bernoulli sums and Renyi Entropy Inequalities. Bernoulli 29 (2023), no. 2, 1578–1599.
Bobkov, Roberto On sharp Sobolev-type inequalities for multidimensional Cauchy measures. Geometric Potential Analysis, a special volume of De Gruyter Series - Advances in Analysis and Geometry, 6. De Gruyter, Berlin, (2022) 135–152.
Melbourne, Roberto Quantiative form of Ball's cube slicing in R^n and equality cases in min-entropy power inequality. Proc. Amer. Math. Soc. 150 (2022), no. 8, 3595–3611.
NB: As pointed out to us by Tomasz Tkocz there is a small error in the proof of Theorem 2. At the top of page 3601 we argue that I(a_{j_o}) \leq \sqrt{2}, an inequality which might be wrong. However, by a continuity argument it is not difficult to proove that I(a_{j_o}) cannot be much larger than \sqrt{2} which allows one to continue the proof at the only price of some constants.
Roberto, Zegarlinski Hypercontractivity for Markov semi-groups. Journal of Functional Analysis 282 (2022), no. 12, Paper No. 109439, 30 pp.
Gozlan, Li, Madiman, Roberto, Samson Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in L1. Potential Analysis, 1-36 (2021).
Gozlan, Roberto, Samson, Tetali Transport proofs of some discrete variants of the Prékopa-Leindler inequality. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 3, 1207–1232.
Bobkov, Gozlan, Roberto, Samson Polar isoperimetry. I: the case of the plane. High dimensional probability VIII, 21–31, Progr. Probab., 74, Birkhäuser/Springer, Cham, (2019).
N. Gozlan, M. Madiman, C. Roberto, P.M. Samson Deviation inequalities for convex functions motivated by the Talagrand conjecture. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 457 (2017), Veroyatnost' i Statistika. 25, 168--182; reprinted in J. Math. Sci. (N.Y.) 238 (2019), no. 4, 453--462.
N. Gozlan, C. Roberto, P-M Samson, Y. Shu, P. Tetali Characterization of a class of weak tranport inequalities on the line. Ann. Inst. Henri Poincaré Probab. Stat. 54 (2018), no. 3, 1667--1693.
N. Gozlan, C. Roberto, P-M Samson, P. Tetali Kantorovich duality for general costs and applications. J. Funct. Anal. 273 (2017), no. 11, 3327--3405.
F. Feo, E. Indrei, M-R. Posteraro, C. Roberto Some remarks on the stability of the log-Sobolev inequality for the Gaussian measure. Potential Anal. 47 (2017), no. 1, 37–52.
Gozlan, Roberto, Samson From dimension free concentration to Poincaré inequality. Calc. Var. Partial Differential Equations 52 (2015), no. 3-4, 899–925.
Cancrini, Martinelli, Roberto, Toninelli Mixing time of a kinetically constrained model on trees: power law scaling at criticality. Proba. Theor. Relat. Fields 161 (2015), no. 1-2, 247–266.
Gozlan, Roberto, Samson, Tetali Displacement convexity of entropy and related inequalities on graphs. Prob. Theor. Relat. Fields 160 (2014), no. 1-2, 47–94.
Bobkov, Gozlan, Roberto, Samson Bounds on the deficit in the logarithmic Sobolev inequality. J. Funct. Anal. 267 (2014), no. 11, 4110–4138.
Faggionato, Roberto, Toninelli Universality for one--dimensional hierarchical coalescence processes with double and triple merges. Annals of Applied Probability (2014), no. 2, 476–525.
Feo, Posteraro, Roberto Quantitative isoperimetric inequalities for log-convex probability measures on the line. J. Math. Anal. Appl. 420 (2014), no. 2, 879–907.
Gozlan, Roberto, Samson Hamilton Jacobi Equations on Metric Spaces and Transport Entropy Inequalities. Rev. Mat. Iberoam. 30 (2014), no. 1, 133–163.
Blondel, Cancrini, Martinelli, Roberto, Toninelli Fredrickson-Andersen one spin facilitated model out of equilibrium. Markov Process. Related Fields 19 (2013), no. 3, 383–406
Gozlan, Roberto, Samson Characterization of Talagrand's transport-entropy inequalities in metric spaces. Ann. Probab. 41 (2013), no. 5, 3112–3139.
Faggionato, Martinelli, Roberto, Toninelli The east model: recent results and new progresses. Markov Process. Related Fields 19 (2013), no. 3, 407–452.
Faggionato, Martinelli, Roberto, Toninelli Universality in one dimensional hierarchical coalescence processes. Annals of Probability 40, no. 4, 1377–1435 (2012).
Faggionato, Martinelli, Roberto, Toninelli Aging through hierarchical coalescence in the East model. Comm. Math. Phys. 309 (2012), no. 2, 459–495.
Foug\`eres, Roberto, Zegarlinski Sub-gaussian measures and associated semilinear problems. Rev. Mat. Iberoam. 28 (2012), no. 2, 305–350.
Gozlan, Roberto, Samson A new characterization of Talagrand's transport-entropy inequalities and applications. Annals of Probability, 39, no. 3, 857--880 (2011).
Gozlan, Roberto, Samson From concentration to logarithmic Sobolev and Poincaré inequalities. J. Funct. Anal. 260, no. 5, 1491--1522 (2011).
Cancrini, Martinelli, Roberto, Toninelli Kinetically constrained lattice gases. Comm. Math. Phys. 297, no. 2, 299--344 (2010).
Cattiaux, Gozlan, Guillin, Roberto Functional inequalities for heavy tails distributions and application to isoperimetry. Electron. J. Probab. 15, no. 13, 346--385 (2010).
Cattiaux, Guillin, Roberto Poincaré inequality and the Lp convergence of semi-groups. Elect. C. Probab., 15, 270-280 (2010).
Roberto Slow decay of Gibbs measures with heavy tails. Probability Theory and Related Fields, Volume 148, Numbers 1-2, 247-268 (2010).
Gozlan, Roberto, Samson Isoperimetry for product of heavy tails distributions. Progress in analysis and its applications, 470–478, World Sci. Publ., Hackensack, NJ, (2010).
Roberto Isoperimetry for product of probability measures: recent results. Markov Processes and Related Fields, 16, no. 4, 617--634 (2010).
Cancrini, Martinelli, Roberto, Toninelli Facilitated spin models: recent and new results. Methods of contemporary mathematical statistical physics. 307--340, Lecture Notes in Math., 1970, Springer, Berlin, (2009).
Cancrini, Martinelli, Roberto, Toninelli Kinetically constrained models. New Trends in Mathematical Physics, p.741-752 Ed: V.Sidoravicius, Springer (2009).
Barthe, Roberto Modified logarithmic Sobolev inequalities on R. Potential Analysis 29, no. 2, 167--193 (2008).
Cancrini, Martinelli, Roberto, Toninelli Kinetically constrained spin models. Probability Theory and Related Fields, 3-4, 459--504 (2008).
Barthe, Cattiaux, Roberto Isoperimetry between exponential and Gaussian. Electron. J. Probab., 12, no. 44, 1212--1237 (electronic) (2007).
Roberto, Zegarlinski Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups. Journal of Functional Analysis 243 (2007), no. 1, 28--66.
Cancrini, Martinelli, Roberto, Toninelli Relaxation times of kinetically constrained spin models with glassy dynamics Journal of Statistical Mechanics: Theory and Experiment, (letter) L03001 (2007).
Barthe, Cattiaux, Roberto Interpolated inequalities between exponential and gaussian, Orlicz hypercontractivity and isoperimetry. Revista Matemática Iberoamericana 22 (2006), no. 3, 993--1067.
Barthe, Cattiaux, Roberto Concentration for independant variables with heavy tails. Applied Mathematic Research eXpress (AMRX), no. 2 (2005), 39--60.
Cancrini, Cesi, Roberto Diffusive long-time behavior of Kawasaki dynamics. Electron. J. Probab., 10 (2005), no. 7, 216--249 (electronic).
Barthe, Roberto Sobolev inequalities for probability measures on the real line. Studia Math., 159 (2003), no. 3, 481--497.
Roberto Path method for the logarithmic Sobolev constant. Combinatorics, Prob. and Comp., 12 (2003), no. 4, 431--455.
Cancrini, Roberto Logarithmic Sobolev constant for the dilute Ising lattice gas dynamics below the percolation threshold. Stochastic Process. Appl., 102 (2002), no. 2, 159--205.
Cancrini, Martinelli, Roberto The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited. Ann. Inst. H. Poincaré Probab. Statist., 38 (2002), no. 4, 385--436.
Gentil, Roberto Spectral gaps for spin systems: some non convex phase examples. Journal of Functional Analysis, 180 (2001), 66--84.
Cancrini, Martinelli, Roberto Spectral gap and logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited. In and out of equilibrium (Mambucaba), 2000, 259--271, Progr. Probab., 51, Birkhauser Boston, Boston, MA, (2002).
Miclo, Roberto Trous spectraux pour certains algorithmes de Métropolis sur R (in french) Séminaire de Probabilités, XXXIV, 336-352, Lecture Notes in Math., 1729, Springer Verlag, Berlin, (2000).

Book:

Ané, Blachère, Chafa&iulm;, Fougères, Gentil, Malrieu, Roberto, Scheffer Sur les inégalités de Sobolev logarithmiques. with a preface of Dominique Bakry et Michel Ledoux. Panoramas et Synthèses 10, Société Mathématique de France, Paris, 2000.

Politics:

Abakumov, Beaulieu, Blanchard, Fradelizi, Gozlan, Host, Jeantheau, Kobylanski, Lecué, Martinez, Meyer, Mourgues, Portal, Ribaud, Roberto, Romon, Roth, Samson, Vandekerkhove, Youssfi The logarithmic Sobolev constant of the Lamplighter. Journal of Mathematical Analysis and Applications 399, no. 2, 576–585 (2013).
Abakumov, Beaulieu, Blanchard, Fradelizi, Gozlan, Host, Jeantheau, Kobylanski, Lecué, Martinez, Meyer, Mourgues, Portal, Ribaud, Roberto, Romon, Roth, Samson, Vandekerkhove, Youssfi Compter et mesurer. Le souci du nombre dans l'évaluation de la production scientifique. [French] La Gazette des Mathématiciens, SMF (2010) et Mediapart (décembre 2010).