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SUMMARY:Diffusions in Liouville Quantum Gravity - Henry Jackson (CCA)
DTSTART:20140507T150000Z
DTEND:20140507T160000Z
UID:TALK52348@talks.cam.ac.uk
CONTACT:Vittoria Silvestri
DESCRIPTION:Many models in statistical physics\, such is the Ising model o
 r percolation\, are defined on graphs. The graphs are usually taken to be 
 deterministic\, regular lattices\, but it is also possible to define the s
 ame models on random graphs. We often want to study properties of the scal
 ing limits of these models - the limits where the lattice size is taken to
  zero.\n\nWhen the graph used is a regular lattice\, the geometry of the s
 caling limit is Euclidean. However\, when we use a random graph\, the geom
 etry of the scaling limit is conjectured to be that of “Liouville quantu
 m gravity\,” which we would like to view as a random Riemann surface.\n\
 nHow to view this surface even as a metric space is still an open question
  but\, due to work by Duplantier & Sheffield and Rhodes & Vargas\, we have
  an area measure for the surface. Despite the fact that we only have an ar
 ea metric for this surface\, it is still possible to construct a Brownian 
 motion on it\, as shown by Berestycki and Garban\, Rhodes & Vargas.\n\nI w
 ill give a brief overview of the construction of the area measure from the
  Gaussian free field\, and some of its properties\, and also the construct
 ion of the Liouville Brownian motion and the specific aspect of it that I 
 am studying.
LOCATION:MR14\, Centre for Mathematical Sciences
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