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SUMMARY:The full extremal process of the discrete Gaussian free field in 2
 D - Oren Louidor (Technion)
DTSTART:20150602T153000Z
DTEND:20150602T163000Z
UID:TALK58980@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:We show the existence of the limit of the full extremal proces
 s of the discrete Gaussian free field in 2D with zero boundary conditions.
  The limit is a clustered Poisson point process with a random intensity me
 asure\, which is conjecturally related to the critical Liouville quantum g
 ravity measure w.r.t. the continuous Gaussian free field. Several corollar
 ies follow directly\, e.g. a natural construction for the super-critical G
 aussian multiplicative chaos and Poisson-Dirichlet statistics\nfor the lim
 iting Gibbs measure - both w.r.t. the CGFF. The proof is based on a novel 
 concentric decomposition of the DGFF which effectively reduces the problem
  to that of finding asymptotics for the probability of a decorated non-hom
 ogenous  \nrandom-walk required to stay positive. Entropic repulsion plays
  a key role in the analysis.\nJoint work with M. Biskup (UCLA)
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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