Gaussian Processes and Mixed Volumes

We prove the following conjecture of Dudley: If the volume exponent of a compact convex and symmetric subset K of a Hilbert space is less than -1, then K is a G.C. set.

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Bibliographic Details
Published in:	The Annals of probability Vol. 15; no. 1; pp. 292 - 304
Main Authors:	Milman, V. D., Pisier, G.
Format:	Journal Article
Language:	English
Published:	Hayward, CA Institute of Mathematical Statistics 01-01-1987 The Institute of Mathematical Statistics
Subjects:	41A46 47B10 60G15 60G17 Banach space continuity of Gaussian process Exact sciences and technology G.C. set Geometry Hilbert spaces Linear transformations Mathematical inequalities Mathematics metric entropy mixed volumes Probability and statistics Probability theory and stochastic processes Quotients Sciences and techniques of general use Stochastic processes Unit ball Volume Entropy Gaussian process
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Description
Summary:	We prove the following conjecture of Dudley: If the volume exponent of a compact convex and symmetric subset K of a Hilbert space is less than -1, then K is a G.C. set.
ISSN:	0091-1798 2168-894X
DOI:	10.1214/aop/1176992271