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SUMMARY:Talagrand's concentration inequality for empirical processes - Ric
 hard Nickl (Cambridge)
DTSTART:20081202T140000Z
DTEND:20081202T150000Z
UID:TALK14301@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:This is an expository talk about a deep probability inequality
  due to Talagrand (Invent. Math. 1996\, cf. Ledoux's book in 2001)\, which
  gives a Prohorov- (and then also Bernstein-) type exponential bound for t
 he concentration of the supremum of an empirical process around its mean. 
 I will try to discuss the following points: A) Some ideas of the proof\, i
 n particular the proof due to Ledoux using logarithmic Sobolev inequalitie
 s\, which is related to the more general "concentration of measure" phenom
 enon. B) Discuss a variety of probabilistic applications\, which should sh
 ow how versatile this inequality is\, in particular that it reproduces mos
 t known exp. inequalities for i.i.d. sums of (possibly Banach-)valued rand
 om variables. C) Discuss recent statistical applications to adaptive estim
 ation\, model selection problems\, Rademacher processes\, and almost sure 
 limit laws (LIL-type results).
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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