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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:Diffusions in Liouville Quantum Gravity - Henry Ja
ckson (CCA)
DTSTART;TZID=Europe/London:20140507T160000
DTEND;TZID=Europe/London:20140507T170000
UID:TALK52348AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52348
DESCRIPTION:Many models in statistical physics\, such is the I
sing model or percolation\, are defined on graphs.
The graphs are usually taken to be deterministic\
, regular lattices\, but it is also possible to de
fine the same models on random graphs. We often wa
nt to study properties of the scaling limits of th
ese models - the limits where the lattice size is
taken to zero.\n\nWhen the graph used is a regular
lattice\, the geometry of the scaling limit is Eu
clidean. However\, when we use a random graph\, th
e geometry of the scaling limit is conjectured to
be that of “Liouville quantum gravity\,” which we
would like to view as a random Riemann surface.\n\
nHow to view this surface even as a metric space i
s still an open question but\, due to work by Dupl
antier & Sheffield and Rhodes & Vargas\, we have a
n area measure for the surface. Despite the fact t
hat we only have an area metric for this surface\,
it is still possible to construct a Brownian moti
on on it\, as shown by Berestycki and Garban\, Rho
des & Vargas.\n\nI will give a brief overview of t
he construction of the area measure from the Gauss
ian free field\, and some of its properties\, and
also the construction of the Liouville Brownian mo
tion and the specific aspect of it that I am study
ing.
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Vittoria Silvestri
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