Abstract
Consider a centered Gaussian measure μ on a separable Banach spaceX. Denote byK the unit ball of the reproducing kernel of μ, and consider a symmetric convex setC ofX. We provide two-sided estimates of μ(C+tK). We determine in a very general setting at which rate for the gauge ofC the variablesY n (2 logn)−1/2 cluster toK, when (Y n ) is an i.i.d. sequence distributed like μ. The rate depends only on the behavior of the function ε→μ(εC) as ε→0.
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Talagrand, M. New Gaussian estimates for enlarged balls. Geometric and Functional Analysis 3, 502–526 (1993). https://doi.org/10.1007/BF01896240
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DOI: https://doi.org/10.1007/BF01896240