The Annals of Probability

Majorizing measures: the generic chaining

Michel Talagrand

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Majorizing measures provide bounds for the supremum of stochastic processes. They represent the most general possible form of the chaining argument going back to Kolmogorov. Majorizing measures arose from the theory of Gaussian processes, but they now have applications far beyond this setting. The fundamental question is the construction of these measures. This paper focuses on the tools that have been developed for this purpose and, in particular, the use of geometric ideas. Applications are given to several natural problems where entropy methods are powerless.

Article information

Ann. Probab. Volume 24, Number 3 (1996), 1049-1103.

First available in Project Euclid: 9 October 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G05: Foundations of stochastic processes 60G15: Gaussian processes
Secondary: 47A40: Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]

Chaining increment condition boundedness of trajectories Gaussian properties majorization measure matchings random restrictions of operators


Talagrand, Michel. Majorizing measures: the generic chaining. Ann. Probab. 24 (1996), no. 3, 1049--1103. doi:10.1214/aop/1065725175.

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