Michel Talagrand

Talagrand has been interested in probability with minimal structure. He has obtained a complete characterization of bounded Gaussian processes in very general settings, and also new methods to bound stochastic processes. He discovered new aspects of the isoperimetric and concentration of measure phenomena for product spaces, by obtaining inequalities which make use of new kind of distances between a point and a subset of a product space. These inequalities show in great generality that a random quantity which depends on many independent variables, without depending too much on one of them, does have only small fluctuations. These inequalities helped to solve most classical problems in probability theory on Banach spaces, and have also transformed the abstract theory of stochastic processes. These inequalities have been successfully used in many applications involving stochastic quantities, like for instance in statistical mechanics (disordered systems), theoretical computer science, random matrices, and statistics (empirical processes). The recent works of Talagrand concern spin glasses mean fields models. His objective is to give a mathematical foundation to numerous remarkable works of physicists in this domain. Talagrand showed for instance recently the validity of the Parisi formula.

• Peccot-Vimont Prize of the French Collège de France (1980)
• Servant Prize of the French Académie des sciences (1985)
• Invited Speaker to the International Congress of Mathematicians (Kyoto 1990)[1]
• Loève Prize in Probability (1995)
• Fermat Prize for mathematical research (1997)
• Corresponding member of the French Academy of Sciences (1997)
• Plenary Speaker to the International Congress of Mathematicians (Berlin 1998)[2]
• Member of the French Academy of Sciences (2004)
• Chevalier of the Order of the Legion of Honor (2011)
• Shaw Prize in mathematics (2019)

• Espaces de Banach faiblement K-analytiques, Annals of Mathematics 110 (1979) 407-438
• Regularity of Gaussian processes, Acta Math. 159 (1987) 99-149
• Some distributions that allow perfect packing, (avec W. Rhee), J. A.C.M. 35 (1988) 564-578
• The Three Space Problem for L1, J. Amer. Math. Soc. 3 (1989) 9-30
• Type, infratype and the Elton-Pajor theorem Invent. Math. 107 (1992 )41-59
• Sharper bounds for Gaussian and empirical processes, Ann. Probab. 22 (1994) 28-76
• Matching theorems and discrepancy computations using majorizing measures, J. Amer. Math. Soc. 7 (1994) 455-537
• Concentration of measure and isoperimetric inequalities in product spaces, Publications I.H.E.S. 81 (1995) 73-205
• Sections of smooth convex bodies via majorizing measures, Acta. Math 175 (1995) 273-306
• The Parisi Formula, Annals of Mathematics 163 (2006) 221-263
• Maharam's Problem, Annals of Mathematics 168 (2008) 981-1009

• M. Talagrand, Pettis Integral and Measure Theory, Memoirs of the AMS no. 307 (1984)
• M. Ledoux & M. Talagrand, Probability in Banach Spaces, Springer-Verlag (1991)
• M. Talagrand, Spin glasses, a Challenge for Mathematicians, Springer-Verlag (2003)
• M. Talagrand, The Generic Chaining, Springer-Verlag (2005)
• M. Talagrand, Mean Field Models for Spin Glasses. Volume I: Basic Examples, Springer-Verlag (2011)
• M. Talagrand, Mean Field Models for Spin Glasses. Volume II: Advanced Replica-Symmetry and Low Temperature, Springer-Verlag (2011)
• M. Talagrand, Upper and Lower Bounds for Stochastic Processes, Springer-Verlag (2014)[3]

• Talagrand's concentration inequality

• The personal web page of Michel Talagrand
• Michel Talagrand at the Mathematics Genealogy Project