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.

pressively wide range of illustrations and applications, and became a central tool ... 13.5 Variations of Nemirovski’s inequality 364 ... were not introduced until the appearance of martingale methods in the 1970’s, see Yurinskii (1976), Maurey (1979), Milman and Schechtman (1986), Shamir ...

Loading..

Tags:

  Ranges, Variations, Wide, Introduced, Wide range

Information

Related search queries