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Majorizing Measures: The Generic Chaining

Michel Talagrand
The Annals of Probability
Vol. 24, No. 3 (Jul., 1996), pp. 1049-1103
Stable URL: http://www.jstor.org/stable/2244967
Page Count: 55
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Majorizing Measures: The Generic Chaining
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Abstract

Majorizing measures provided 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 the 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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