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SUMMARY:Isomorphism theorems and the sign cluster geometry of the Gaussian
  free field - Pierre-Francois Rodriguez (IHES\, Paris)
DTSTART:20190528T140000Z
DTEND:20190528T150000Z
UID:TALK123826@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We consider the Gaussian free field (GFF) on a large class of 
 transient weighted graphs G\, and prove that its sign clusters contain an 
 infinite connected component. In fact\, we show that the sign clusters fal
 l into a regime of strong supercriticality\, in which two infinite sign cl
 usters dominate (one for each sign)\, and finite sign clusters are necessa
 rily tiny\, with overwhelming probability. Examples of graphs G belonging 
 to this class include cases in which the random walk on G exhibits anomalo
 us diffusive behavior. Among other things\, our proof exploits a certain r
 elation (isomorphism theorem) relating the GFF to random interlacements\, 
 which form a Poissonian soup of bi-infinite random walk trajectories.\nOur
  findings also imply the existence of a nontrivial percolating regime for 
 the vacant set of random interlacements on G. \n\nBased on joint work with
  A. Prévost and A. Drewitz.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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