The concentration of measure phenomenon
- Michel Ledoux (Université Toulouse III)
Measure concentration ideas developed during the last century in various parts of mathematics, including functional analysis, probability theory and statistical mechanics, areas typically dealing with models involving an infinite number of variables. After several early observations, the real birth of measure concentration took place in the early seventies with the new proof by V. Milman of Dvoretzky's theorem on spherical sections of convex bodies in high dimension. Since then, the concentration of measure phenomenon spred out to a wide range of illustrations and applications, and became a central tool and viewpoint in the quantitative analysis of asymptotics properties in numerous topics of interest including geometric analysis, probability theory, statistical mechanics, mathematical statistics and learning theory, random matrix theory, randomized algorithms, complexity etc. The talk will feature basics aspects and some of these illustrations.