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.
ary new look at independence. Viewing namely random variables depending (in a smooth way) on the in ... Author Index 469. 1 INTRODUCTION The topic of this book is the study of random uctuations of functions of inde-pendent random variables. Concentration inequalities quantify such …
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