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SUMMARY:Cauchy-Schwarz Principles for uniform entropy - Ramon van Handel\,
  Princeton University 
DTSTART:20140623T110000Z
DTEND:20140623T113000Z
UID:TALK53095@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:Giné and Zinn have given a Gaussian characterization of class
 es of functions for which the empirical process satisfies the central limi
 t theorem uniformly over all distributions of the underlying variables. A 
 central object that arises in this characterization is the uniform Gaussia
 n width\, which can be upper bounded by the Koltchinskii-Pollard uniform e
 ntropy integral. In simple examples\, however\, the uniform Gaussian width
  proves to behave in a strictly better manner than might be expected from 
 such computations. This phenomenon is not due to the inefficiency of class
 ical chaining arguments\, as might be expected in view of the majorizing m
 easure theory\, but rather due to the fact that the uniform entropy can gr
 ow at a strictly faster rate than the entropy with respect to any fixed di
 stribution. In this talk I will aim to explain this phenomenon\, its conne
 ction with combinatorial parameters\, and whatever understanding I have at
  the present time (which is very limited) about the occurence of such beha
 vior in general settings.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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