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CATEGORIES:Cambridge Centre for Analysis talks
SUMMARY:The Schramm-Loewner Evolution and the Gaussian Fre
e Field - Dr Jason Miller\, MIT
DTSTART;TZID=Europe/London:20121106T150000
DTEND;TZID=Europe/London:20121106T160000
UID:TALK39831AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39831
DESCRIPTION:The Schramm-Loewner evolution (SLE) is the canonic
al model of a non-crossing conformally invariant r
andom curve\, introduced by Oded Schramm in 1999 a
s a candidate for the scaling limit of loop erased
random walk and the interfaces in critical percol
ation. The development of SLE has been one of the
most exciting areas in probability over the last d
ecade because Schramm's curves have now been rigor
ously shown to describe the limiting interfaces of
a number of different two-dimensional models from
statistical mechanics. Work on this topic has so
far led to two Fields medals (Werner\, 2006 and Sm
irnov\, 2010). \nThe first part of this talk will
be a basic introduction to SLE. In the second part
of the talk\, I will describe the work of Sheffie
ld\, Schramm-Sheffield\, and Dubédat on how SLEs a
re related to a certain random geometry which is g
enerated by the GFF. Namely\, SLE can be realized
as the flow lines of the random vector field eih/x
where h is a GFF and x > 0.
LOCATION:MR2
CONTACT:CCA
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