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July 1996 Majorizing measures: the generic chaining
Michel Talagrand
Ann. Probab. 24(3): 1049-1103 (July 1996). DOI: 10.1214/aop/1065725175


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.


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Michel Talagrand. "Majorizing measures: the generic chaining." Ann. Probab. 24 (3) 1049 - 1103, July 1996.


Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0867.60017
MathSciNet: MR1411488
Digital Object Identifier: 10.1214/aop/1065725175

Primary: 60G05 , 60G15
Secondary: 47A40

Keywords: boundedness of trajectories , Chaining , Gaussian properties , increment condition , majorization measure , Matchings , random restrictions of operators

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 3 • July 1996
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