Michel Ledoux

Professeur de Mathématiques / Professor of Mathematics

Institut de Mathématiques de Toulouse
Unité Mixte de Recherche CNRS 5219
Université de Toulouse
Université Paul-Sabatier (Toulouse III)

• Editeur associé / Associate Editor
  • Applied Mathematics Research eXpress
  • ALEA
  • Probability Theory and Related Fields
  • Electronic Journal of Probability - Electronic Communications in Probability
  • IMS Collections
• Membre / Member of the Toulouse Node of the European Network Phenomena in High Dimensions
• Membre / Member of the ANR project GRANdes Matrices Aléatoires
• Membre / Member of the ANR project Dissipative EVOLutions and convergence to equilibrium
• Co-Organisateur / Co-Organizer with A. Kuijlaars (Leuwen) of the conference Matrices Aléatoires / Random Matrices Luminy, France (30 October - 3 November 2006)
• Co-Organisateur / Co-Organizer of the semester program Complex Stochastic Systems: Discrete vs. Continuous Bonn, Germany (September 2007 - February 2008)
• Co-Organisateur / Co-Organizer with F. Barthe (Toulouse) of the session Etats de la Recherche de la SMF : Géométrie et Probabilités en Interaction Toulouse, France (20 - 23 May 2008)
  
• 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 ( ps , pdf )
  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
  
• 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 (ps, pdf )
  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 ( pdf )
  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 ( pdf )
  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 ( ps , pdf )
  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 ( ps , pdf )
  Séminaire de Probabilités XXXVII. Lecture Notes in Math. 1832, 360-369. Springer (2003). MR2053053
  
• Ledoux, M.
  Measure concentration, transportation cost, and functional inequalities ( pdf )
  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 ( pdf )
  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 ( pdf )
  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
  
• Bakry, D. , Ledoux, M., Wang, F.-Y.
  Perturbations of functional inequalities using growth conditions ( pdf )
  J. Maths Pures Appl. 87, 394-407 (2007). MR2317340
  
• Ledoux, M., Oleszkiewicz, K.
  On measure concentration of vector valued maps ( pdf )
  Bull. Pol. Acad. Sci. Math. 55, 261-278 (2007). MR2346103
  
• Cohen, S. , Lacaux, C. , Ledoux, M.
  A general framework for simulation of fractional fields ( pdf )
  Stochastic Process. Appl. 118, 1489-1517 (2008). MR2442368
  
• Ledoux, M.
  Complex Hermite polynomials: from the semi-circular law to the circular law ( pdf )
  Communications on Stochastic Analysis 2, 27-32 (2008). MR2446909
  
• Bobkov, S. , Ledoux, M.
  From Brunn-Minkowski to sharp Sobolev inequalities ( pdf )
  Annali di Matematica Pura ed Applicata 187, 369-384 (2008). MR2393140
  
• Ledoux, M.
  Géométrie des espaces métriques mesurés : les travaux de Lott, Villani, Sturm ( pdf )
  Séminaire Bourbaki (2008).
  
• Ledoux, M.
  A recursion formula for the moments of the Gaussian Orthogonal Ensemble ( pdf )
  Annales Inst. H. Poincaré 45, 754-769 (2009) .
  
• Bobkov, S. , Ledoux, M.
  Weighted Poincaré-type inequalities for Cauchy and other convex measures ( pdf )
  Ann. Probability 37, 403-427 (2009). MR2510011
  
• Chatterjee, S. , Ledoux, M.
  An observation about submatrices
  Elect. Comm. in Probability 14, 495-500 (2009).
  
• Ledoux, M., Popescu, I.
  Mass transportation proofs of free functional inequalities, and free Poincaré inequalities ( pdf )
  J. Funct. Anal. 257, 1175-1221 (2009). MR2535467
  
• Bobkov, S. , Ledoux, M.
  On weighted isoperimetric and Poincaré-type inequalities ( pdf )
  IMS Collections. High Dimensional Probability V, vol. 5, 1-29 (2009)
  
• Barthe, F. , Cordero-Erausquin, D. , Ledoux, M., Maurey, B.
  Correlation and Brascamp-Lieb inequalities for Markov semigroups ( pdf )
  Preprint (2009).
  
• Cordero-Erausquin, D. , Ledoux, M.
  The geometry of Euclidean convolution inequalities and entropy ( pdf )
  To appear in Proc. Amer. Math. Soc. (2009).
  
• Ledoux, M.
  From concentration to isoperimetry: semigroup proofs ( pdf )
  Preprint (2009).
  
• Ledoux, M., Rider, B.
  Small deviations for beta ensembles ( pdf )
  Preprint (2010).
  

Livres / Books

• Ledoux, M., Talagrand, M.
  Probability in Banach spaces
  Ergebnisse der Mathematik. Springer (1991). Second printing (2002). MR1102015
  
• Ledoux, M.
  Isoperimetry and Gaussian analysis ( ps , pdf )
  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 ps , pdf )
  Mathematical Surveys and Monographs 89, American Mathematical Society (2001). Second printing (2005). MR1849347
  

Exposés de conférence / Conference talks

• Fith European Congress of Mathematics, Amsterdam 2008.
  Markov operators, classical orthogonal polynomial ensembles, and random matrices ( pdf )
  
• The state of Geometry and Functional Analysis (in honor of Professor Vitali Milman's 70th birthday), Tel Aviv 2009.
  Measure concentration, functional inequalities and curvature of metric measure spaces ( pdf )
  

Doctorants / Doctoral Students

• Wolfgang Stolz (1995)
• Eric Fontenas (1996)
• Mireille Capitaine (1996)
• Paul-Marie Samson (1998)
• Cécile Ané (2000)
• Ivan Gentil (2001)
• Djalil Chafaï (2002)
• Christophe Brouttelande (2003)
• Yan Doumerc (2005)
• Anne-Séverine Boudou (en co-tutelle avec P. Dai Pra, Padova) (2005)
• Delphine Féral (2006)
• Jean-Paul Ibrahim
• Erwan Hillion
• Sandrine Dallaporta
• Adrien Hardy (en co-tutelle avec A. Kuijlaars, Leuwen)

Publications pédagogiques

• Barbe, Ph. , Ledoux, M.
  Probabilité
  De la Licence à l'Agrégation. Editions Espaces 34, Belin (1998). Nouvelle édition EDP Sciences (2007).
• Toulouse, P. S.
  Thèmes de Probabilités et Statistique
  Dunod (1999).