Abstract
We present a generalization of Slepian's lemma and Fernique's theorem. We show how these can be easily applied to give a new proof, with improved estimates, of Dvoretzky’s theorem on the existence of “almost” spherical sections for arbitrary convex bodies inR N, while avoiding the isoperimetric inequality.
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Supported by Technion V.P.R. grant #100–526, and fund for the promotion of research at the Technion #100–559.
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Gordon, Y. Some inequalities for Gaussian processes and applications. Israel J. Math. 50, 265–289 (1985). https://doi.org/10.1007/BF02759761
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DOI: https://doi.org/10.1007/BF02759761