Transcription of Concentration inequalities
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Concentration inequalities
Concentration inequalitiesA nonasymptotic theory of independenceSt ephane BoucheronParis 7G abor LugosiICREA and Universitat Pompeu FabraPascal MassartOrsayCLARENDON Concentration ideas developed during the last century in various partsof mathematics, including functional analysis, probability theory and statisticalmechanics, areas typically dealing with models involving an infinite number ofvariables. After early observations, and in particular a geometric interpretationof the law of large numbers by E. Borel, the real birth of measure concentrationtook place in the early seventies with the new proof by V. Milman, relying onL evy s inequality (of isoperimetric nature), of Dvoretzky s theorem on sphericalsections of convex bodies in high dimension. The inherent concept of measureconcentration emphasized by V. Milman through this proof turned out as oneof the main achievements of analysis of the second part of the last century.
statistical mechanics, mathematical statistics and learning theory, random ma-trix theory or quantum information theory, stochastic dynamics, randomized algorithms, complexity etc. The book by S. Boucheron, G. Lugosi and P. Massart is a most welcome and complete account on the modern developments of concentration inequalities
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