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Concentration Inequalities – A Nonasymptotic Theory of Independence - Oxford Scholarship Online
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Concentration Inequalities: A Nonasymptotic Theory of Independence

Stéphane Boucheron, Gábor Lugosi, and Pascal Massart


This monograph presents a mathematical theory of concentration inequalities for functions of independent random variables. The basic phenomenon under investigation is that if a function of many independent random variables does not depend too much on any of them then it is concentrated around its expected value. This book offers a host of inequalities to quantify this statement. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities, transportation arguments, to information theory. Applications to the st ... More

Keywords: concentration inequalities, entropy method, concentration of measure, isoperimetric problems, empirical processes, transportation method, influences

Bibliographic Information

Print publication date: 2013 Print ISBN-13: 9780199535255
Published to Oxford Scholarship Online: May 2013 DOI:10.1093/acprof:oso/9780199535255.001.0001


Affiliations are at time of print publication.

Stéphane Boucheron, author
Laboratoire de Probabilités et Modèles Aléatoires, Université Paris-Diderot

Gábor Lugosi, author
ICREA Research Professor, Pompeu Fabra University

Pascal Massart, author
Laboratoire de Mathématiques, Université Paris Sud and Institut Universitaire de France