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Majorizing measures: the generic chaining

1996; Institute of Mathematical Statistics; Volume: 24; Issue: 3 Linguagem: Inglês

10.1214/aop/1065725175

2168-894X

Michel Talagrand,

Advanced Banach Space Theory

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.