Michel Ledoux

Editorial Boards

• Chief Editor
  • Electronic Journal of Probability
• Associate Editor
  • Electronic Communications in Probability
  • ALEA
  • Applied Mathematics Research eXpress
  • IMS Collections

Networks, Conferences

• Member of the Toulouse Node of the European Network (2004 - 08) Phenomena in High Dimensions.
• Membre du projet ANR GRANdes Matrices Aléatoires.
• Membre du projet ANR Dissipative EVOLutions and convergence to equilibrium.
• Membre du projet ANR Géométrie des mesures convexes et discrètes GeMeCoD.
• Co-Organizer with A. Kuijlaars (Leuven) of the conference Matrices Aléatoires / Random Matrices , Luminy, France (30 October - 3 November 2006).
• Co-Organizer of the semester program Complex Stochastic Systems: Discrete vs. Continuous , Bonn, Germany (September 2007 - February 2008).
• Co-Organisateur avec F. Barthe (Toulouse) de la session des Etats de la Recherche de la SMF : Géométrie et Probabilités en Interaction , Toulouse, France (20 - 23 May 2008).
• Speaker at the Summer School Optimal mass transport and geometric inequalities , Riezlern, Kleinwalsertal, Austria (20 - 24 September 2010).
• Co-Organizer with M. Rudelson (Missouri) and G. Schechtman (Weizman Institute) of the conference Random Matrices, Geometric Functional Analysis and Algorithms , Oberwolfach, Germany (1 - 7 May 2011).
• Member of the Scientific Committee of the 5th International Conference on Stochastic Analysis and its Applications , Bonn, Germany (5-9 September 2011).
• Co-Organizer with J.-R. Chazottes (Ecole Polytechnique, France) and F. Redig (Delft, Netherlands) of the conference Concentration inequalities and their applications , Luminy, France (23 - 27 January 2012).
• Speaker at the ERC School Analysis and Geometry in Metric Measure Spaces , Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy (7-11 May 2012).
• Member of the Scientific Committee of the 6th International Conference on Stochastic Analysis and its Applications , Bedlewo, Poland (9-15 September 2012).
• Affiliations
  • Membre de la Société Mathématique de France
  • Member of the European Mathematical Society
  • Member of the Institute of Mathematical Statistics

Principaux centres d'intérêts

• Probabilités, isopérimétrie, concentration de la mesure, grandes déviations
• Matrices aléatoires, polynômes orthogonaux, probabilités libres
• Inégalités de Sobolev logarithmiques, inégalités de transport, équations de Hamilton-Jacobi
• Analyse, noyaux de la chaleur, inégalités fonctionnelles, géométrie des semigroupes de Markov et géométrie riemannienne, espaces de chemins et de lacets
• Mécanique statistique, verres de spins, mesures de Gibbs
• Mesures et processus gaussiens, calcul des probabilités dans les espaces de Banach, convexité

Main research interests

• Probability, isoperimetry, concentration of measure, large deviations
• Random matrices, orthogonal polynomials, free probability
• Logarithmic Sobolev inequalities, transportation cost inequalities, Hamilton-Jacobi equations
• Analysis, heat kernels, functional inequalities, geometry of Markov semigroups and Riemannian geometry, path and loop spaces
• Statistical mechanics, spin glasses, Gibbs measures
• Gaussian measures and processes, probability in Banach spaces, convexity

Sélection de publications récentes / Selected recent publications

• Ledoux, M.
  Isopérimétrie et inégalités de Sobolev logarithmiques gaussiennes
  C. R. Acad. Sci. Paris 306, 79-82 (1988). MR0929114
  
• Ledoux, M.
  Inégalités isopérimétriques en analyse et probabilités
  Séminaire Bourbaki. Astérisque 216, 343-375 (1993). MR1246403
  
• Ledoux, M.
  A simple analytic proof of an inequality by P. Buser
  Proc. Amer. Math. Soc. 121, 951-959 (1994). MR1186991
  
• Coulhon, T. , Ledoux, M.
  Isopérimétrie, décroissance du noyau de la chaleur et transformations de Riesz : un contre-exemple
  Ark. Mat. 32, 63-77 (1994). MR1277920
  
• Ledoux, M.
  Remarks on logarithmic Sobolev constants, exponential integrability and bounds on the diameter
  J. Math. Kyoto Univ. 35, 211-220 (1995). MR1346225
  
• Bakry, D. , Coulhon, T. , Ledoux, M., Saloff-Coste, L.
  Sobolev inequalities in disguise
  Indiana Math. J. 44, 1034-1074 (1995). MR1386760
  
• Ledoux, M.
  L'algèbre de Lie des gradients itérés d'un générateur markovien - Développements de moyennes et entropies
  Ann. scient. Ec. Norm. Sup. 28, 435-460 (1995). MR1334608
  
• Bakry, D. , Ledoux, M.
  Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
  Duke Math. J. 85, 253-270 (1996). MR1412446
  
• Bakry, D. , Ledoux, M.
  Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
  Invent. math 123, 259-281 (1996). MR1374200
  
• Ledoux, M.
  On Talagrand's deviation inequalities for product measures
  ESAIM Probability and Statistics 1, 63-87 (1996). MR1399224
  
• Bobkov, S. , Ledoux, M.
  Poincaré's inequalities and Talagrands's concentration phenomenon for the exponential distribution
  Probab. Theor. Relat. Fields 107, 383-400 (1997). MR1440138
  
• Capitaine, M. , Hsu, E. P. , Ledoux, M.
  Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces
  Elect. Comm. in Probability 2, 71-81 (1999). MR1484557
  
• Ledoux, M.
  On manifolds with non-negative Ricci curvature and Sobolev inequalities
  Communications in Analysis and Geometry 7, 347-353 (1999). MR1685586
  
• Ledoux, M.
  Concentration of measure and logarithmic Sobolev inequalities
  Séminaire de Probabilités XXXIII. Lecture Notes in Math. 1709, 120-216. Springer (1999). MR1767995
  
• Del Moral, P. , Ledoux, M.
  Convergence of empirical processes for interacting particle systems with applications to non-linear filtering
  J. Theoretical Probability 13, 225-257 (2000). MR1744985
  
• Ledoux, M.
  The geometry of Markov diffusion generators
  Ann. Fac. Sci. Toulouse IX, 305-366 (2000). MR1813804
  
• Bobkov, S. , Ledoux, M.
  From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
  Geom. funct. anal. 10, 1028-1052 (2000). MR1800062
  
• Ledoux, M.
  On the distribution of overlaps in the Sherrington-Kirkpatrick spin glass model
  J. Stat. Phys. 100, 871-892 (2000). MR1798547
  
• Djadli, Z. , Hebey, E. , Ledoux, M.
  Paneitz-type operators and applications
  Duke Math. J. 104, 129-169 (2000). MR1769728
  
• Ledoux, M.
  Logarithmic Sobolev inequalities for unbounded spin systems revisited
  Séminaire de Probabilités XXXV. Lecture Notes in Math. 1755, 1167-194. Springer (2001). MR1837286
  
• Bobkov, S. , Gentil, I. , Ledoux, M.
  Hypercontractivity of Hamilton-Jacobi equations
  J. Math. Pures Appl. 80, 669-696 (2001). MR1846020
  
• Ledoux, M., Lyons, T. , Qian, Z.
  Lévy area of Wiener processes in Banach spaces
  Ann. Probab. 30, 546-578 (2002). MR1905851
  
• Benaïm, M. , Ledoux, M., Raimond, O.
  Self-interacting diffusions
  Probab. Theor. Rel. Fields 122, 1-41 (2002). MR1883716
  
• Ledoux, M., Qian, Z. , Zhang, T.
  Large deviations and support theorem for diffusion processes via rough paths
  Stoch. Proc. Appl. 102, 265-283 (2002). MR1935127
  
• Ledoux, M.
  On improved Sobolev embedding theorems
  Math. Res. Letters 10, 659-669 (2003). MR2024723
  
• Ledoux, M.
  A remark on hypercontractivity and tail inequalities for the largest eigenvalues of random matrices
  Séminaire de Probabilités XXXVII. Lecture Notes in Math. 1832, 360-369. Springer (2003). MR2053053
  
• Ledoux, M.
  Measure concentration, transportation cost, and functional inequalities
  Instructional Conference on Combinatorial Aspects of Mathematical Analysis, Edinburgh, 25 March-5 April 2002 and Summer School on Singular Phenomena and Scaling in Mathematical Models, Bonn, 10-13 June 2003.
  
• Ledoux, M.
  Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case
  Elect. Journal in Probability 9, 177-208 (2004). MR2041832
  
• Ledoux, M.
  Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The discrete case
  Elect. Journal in Probability 10, 1116-1146 (2005). MR2164041
  
• Ledoux, M.
  A (one-dimensional) free Brunn-Minkowski inequality
  C. R. Acad. Sciences, Paris, 340, 301-304 (2005). MR2121895
  
• Bakry, D. , Ledoux, M.
  A logarithmic Sobolev form of the Li-Yau parabolic inequality
  Revista Mat. Iberoamericana 22, 683-702 (2006). MR2294794
  
• Ledoux, M.
  Deviation inequalities on largest eigenvalues
  Summer School on the Connections between Probability and Geometric Functional Analysis, Jerusalem, 14-19 June 2005. Geometric Aspects of Functional Analysis, Israel Seminar 2004-2005. Lecture Notes in Math. 1910, 167-219. Springer (2007). MR2349607
  
• Ledoux, M., Oleszkiewicz, K.
  On measure concentration of vector valued maps
  Bull. Pol. Acad. Sci. Math. 55, 261-278 (2007). MR2346103
  
• Cohen, S. , Lacaux, C. , Ledoux, M.
  A general framework for simulation of fractional fields
  Stochastic Process. Appl. 118, 1489-1517 (2008). MR2442368
  
• Ledoux, M.
  Complex Hermite polynomials: from the semi-circular law to the circular law
  Communications on Stochastic Analysis 2, 27-32 (2008). MR2446909
  
• Bobkov, S. , Ledoux, M.
  From Brunn-Minkowski to sharp Sobolev inequalities
  Annali di Matematica Pura ed Applicata 187, 369-384 (2008). MR2393140
  
• Ledoux, M.
  Géométrie des espaces métriques mesurés : les travaux de Lott, Villani, Sturm
  Séminaire Bourbaki. Astérisque 326, 257-280 (2009). MR2605325
  
• Ledoux, M.
  A recursion formula for the moments of the Gaussian Orthogonal Ensemble
  Annales Inst. H. Poincaré 45, 754-769 (2009). MR2548502
  
• Bobkov, S. , Ledoux, M.
  Weighted Poincaré-type inequalities for Cauchy and other convex measures
  Ann. Probability 37, 403-427 (2009). MR2510011
  
• Chatterjee, S. , Ledoux, M.
  An observation about submatrices
  Elect. Comm. in Probability 14, 495-500 (2009). MR2559099
  
• Ledoux, M., Popescu, I.
  Mass transportation proofs of free functional inequalities, and free Poincaré inequalities
  J. Funct. Anal. 257, 1175-1221 (2009). MR2535467
  
• Bobkov, S. , Ledoux, M.
  On weighted isoperimetric and Poincaré-type inequalities
  IMS Collections. High Dimensional Probability V, vol. 5, 1-29 (2009).
  
• Cordero-Erausquin, D. , Ledoux, M.
  The geometry of Euclidean convolution inequalities and entropy
  Proc. Amer. Math. Soc. 138, 2755-2769 (2010). MR2644890
  
• Ledoux, M., Rider, B.
  Small deviations for beta ensembles
  Elect. J. Probability 15, 1319-1343 (2010). MR2678393
  
• Barthe, F. , Cordero-Erausquin, D. , Ledoux, M., Maurey, B.
  Correlation and Brascamp-Lieb inequalities for Markov semigroups
  Int. Math. Res. Not. IMRN 10, 2177-2216 (2011). MR2806562
  
• Ledoux, M.
  From concentration to isoperimetry: semigroup proofs
  Contemp. Math. 505, Amer. Math. Soc. , 155-166 (2011). MR2858471
  
• Ledoux, M.
  Chaos of a Markov operator and the fourth moment condition
  To appear in Ann. Probability (2011).
  
• Cordero-Erausquin, D. , Ledoux, M.
  Hypercontractive measures, Talagrand's inequality, and influences
  (2011).
  
• Ledoux, M., Popescu, I.
  The one dimensional free Poincaré inequality
  (2011).
  
• Boche, H. , Farell, B. , Ledoux, M., Wiese, M.
  Expected supremum of a random linear combination of shifted kernels
  (2011).
  
• Gigli, N. , Ledoux, M.
  From log Sobolev to Talagrand: a quick proof
  (2012).
  

Livres / Books

• Ledoux, M., Talagrand, M.
  Probability in Banach spaces
  Ergebnisse der Mathematik. Springer (1991). Second printing (2002). Classics in Mathematics. Springer (2011). MR1102015
  
• Ledoux, M.
  Isoperimetry and Gaussian analysis
  Ecole d'été de Probabilités de St-Flour 1994. Lecture Notes in Math. 1648, 165-294. Springer (1996). MR1600888
  
• Ledoux, M.
  The concentration of measure phenomenon. Introduction, References
  Mathematical Surveys and Monographs 89, American Mathematical Society (2001). Second printing (2005). MR1849347
  
• Bakry, D. , Ledoux, M., Saloff-Coste, L.
  Markov Semigroups at Saint-Flour. Series: Probability at Saint-Flour (2012). Reprint of lectures originally published in the Lecture Notes in Mathematics volumes 1581 (1994), 1648 (1996) and 1665 (1997).
  
• Bakry, D. , Gentil, I. , Ledoux, M.
  Analysis and geometry of Markov diffusion semigroups.
  In preparation (2012).