Michel Talagrand

Michel Pierre Talagrand (born 15 February 1952) is a French mathematician.

Docteur ès sciences since 1977, he has been, since 1985, Directeur de Recherches at CNRS and a member of the Functional Analysis Team of the Institut de Mathématique of Paris.

Talagrand was elected as correspondent of the Académie des sciences of Paris in March 1997, and then as a full member in November 2004, in the Mathematics section.

Talagrand studies mainly functional analysis and probability theory and their applications.

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).

Talagrand commented in the introduction to his two volume monograph on mean field models of spin glasses:

"More generally theoretical physicists have discovered wonderful new areas of mathematics, which they have explored by their methods. This book is an attempt to correct this anomaly by exploring these areas using mathematical methods, and an attempt to bring these marvelous questions to the attention of the mathematical community."

In particular, the monograph offers an exposition of Talagrand's proof of the validity of the Parisi formula.