Cyril ROBERTO

My collaborators: Cécile Ané, Dominique Bakry , Franck Barthe , Sébastien Blachère, Nicoletta Cancrini , Patrick Cattiaux, Filippo Cesi, Djalil Chafaï, Pierre Fougères, Ivan Gentil , Nathael Gozlan, Arnaud Guillin , Michel Ledoux , Florent Malrieu , Fabio Martinelli , Laurent Miclo, Gregory Scheffer, Cristina Toninelli, Boguslaw Zegarlinski .

Workshop

FUNCTIONAL INEQUALITIES AND CONVEX GEOMETRY. December 1-4, 2008, Marne-La-Vallée, France.
FROM DYNAMICAL SYSTEMS TO STATISTICAL MECHANICS. February 4 - march 7, 2008, CIRM, Marseille, France.
FUNCTIONAL INEQUALITIES AND APPLICATIONS December 4-5, 2007, Marne-La-Vallée.

Preprints

Cattiaux, Gozlan, Guillin, Roberto Functional inequalities for heavy tails distributions and application to isoperimetry Preprint (2008).
Barthe, Roberto . Modified logarithmic Sobolev inequalities on R. To appear in Potential Analysis (2008).

Publications

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 (1), 28--66 (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. Dedicated to Professor Aleksander Pe\l czy\'nski on the occasion of his 70th birthday (Polish). 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.
Miclo, Roberto. Trous spectraux pour certains algorithmes de Métropolis sur $\dR$. (in french) Séminaire de Probabilités, XXXIV, 336-352, Lecture Notes in Math., 1729, Springer Verlag, Berlin, (2000).

Book

Ané, Blachère, Chafaï, Fougères, Gentil, Malrieu, Roberto, Scheffer. Sur les inégalités de Sobolev logarithmiques. with a preface by Dominique Bakry and Michel Ledoux. Panoramas et Synthèses 10, Société Mathématique de France, Paris, (2000). The dedicated web page .

Proceeding

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, Birkh�user Boston, Boston, MA, (2002).

Letter

Cancrini, Martinelli, Toninelli, Roberto. Relaxation times of Kinetically constrained spins models with glassy dynamics. Journal of Statistical Mechanics: Theory and Experiment, (letter) L03001 (2007).

Unbublished Notes

Roberto. Inégalités de Hardy avec poids. (french), (2001).
Cancrini, Roberto. Density-density correlation for conservative systems in dimension one. (2004). (please send me an email if you need the file).
Roberto. Path Method, a general approach. (2004) (please send me an email if you need the file).