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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Pointwise multiplication of random Schwartz distri
butions with Wilson&\;#39\;s operator product e
xpansion - Abdelmalek Abdesselam (University of Vi
rginia)
DTSTART;TZID=Europe/London:20181022T133000
DTEND;TZID=Europe/London:20181022T143000
UID:TALK112669AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/112669
DESCRIPTION:I will present a general theorem for the multiplic
ation of random distributions which is similar in
spirit to the construction of local Wick powers of
a Gaussian field. However\, this theorem is much
more general in scope and applies to non-Gaussian
measures\, even without translation invariance and
in the presence of anomalous scaling\, provided t
he random fields involved are less singular than w
hite noise. Conjecturally\, the construction of th
e energy field of the 3D Ising scaling limit as a
square of the spin field should fall within the pu
rview of the theorem. Our construction involves mu
ltiplying mollified distributions followed by suit
able additive and multiplicative renormalizations
before a proof of almost-sure convergence when the
mollification is removed. The main tools for the
proof are combinatorial estimates on moments. The
main hypothesis for the theorem is Wilson'\;s O
PE with precise quantitative bounds for pointwise
correlations at noncoinciding points. I will also
explain how the theorem works on the example of a
simple conformal field theory of mean field type\,
namely\, the fractional Gaussian field.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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