A simple proof of the blowing-up lemma (Corresp.)

Marton, Katalin

doi:10.1109/tit.1986.1057176

Cited by 163 publications

(156 citation statements)

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“…This link between transportation cost inequality and concentration inequality was first noticed by K. Marton, see [13]. Her result extends as follows.…”

Section: Some Applications: Concentration Of Measure and Deviations Osupporting

confidence: 66%

A large deviation approach to some transportation cost inequalities

Gozlan

Léonard

2006

Probab. Theory Relat. Fields

106

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Abstract. New transportation cost inequalities are derived by means of elementary large deviation reasonings. Their dual characterization is proved; this provides an extension of a well-known result of S. Bobkov and F. Götze. Their tensorization properties are investigated. Sufficient conditions (and necessary conditions too) for these inequalities are stated in terms of the integrability of the reference measure. Applying these results leads to new deviation results: concentration of measure and deviations of empirical processes.

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“…This link between transportation cost inequality and concentration inequality was first noticed by K. Marton, see [13]. Her result extends as follows.…”

Section: Some Applications: Concentration Of Measure and Deviations Osupporting

confidence: 66%

A large deviation approach to some transportation cost inequalities

Gozlan

Léonard

2006

Probab. Theory Relat. Fields

106

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“…Indeed, the first general concentration result seems to have been proved and used in this context, by Ahlswede, Ga.cs and Korner [1] in 1976. Their concentration result, the 'blowing-up lemma', was sharpened by Csiszar and Korner [17], and then in 1986 Marton [40] gave a simple and elegant proof. This result resembled Theorem 3.5 above, though with a worse constant in the exponent.…”

Section: Ideas From Information Theorymentioning

confidence: 99%

“…However, they are very elegant and powerful, and so we try here to give a flavour of the method. We shall show how they give a very different proof of Theorem 3.5, following [40,41].…”

Section: Ideas From Information Theorymentioning

confidence: 99%

Concentration

McDiarmid

1998

Algorithms and Combinatorics

404

141

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Summary.Upper bounds on probabilities of large deviations for sums of bounded independent random variables may be extended to handle functions which depend in a limited way on a number of independent random variables. This 'method of bounded differences' has over the last dozen or so years had a great impact in probabilistic methods in discrete mathematics and in the mathematics of operational research and theoretical computer science. Recently Talagrand introduced an exciting new method for bounding probabilities of large deviations, which often proves superior to the bounded differences approach. In this chapter we introduce and survey these two approaches and some of their applications.

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“…Such transportation inequalities have been introduced for :=1 by K. Marton [Ma1]. On the basis of (1.4), she established concentration inequalities for discrete product measures (and, furthermore, for distributions of certain Markov processes, [Ma2]), of the form…”

Section: Introductionmentioning

confidence: 99%