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SUMMARY:Local time at zero metric associated to a GFF on a cable graph. - 
 Titus Lupu (ETH Zurich)
DTSTART:20161011T153000Z
DTEND:20161011T163000Z
UID:TALK67741@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We will consider an electrical network and replace the discret
 e edges by continuous lines of appropriate length. This is a cable graph. 
 The discrete Gaussian Free Field (GFF) on the network can be interpolated 
 to a continuous process on the cable graph and which satisfies the Markov 
 property. This is the cable GFF. We will consider a pseudo-metric on the c
 able graph related to the local time at zero of the cable GFF. We will com
 pute some universal explicit laws for this metric and show a generalizatio
 n on the cable graph of Lévy’s theorem for the local time at zero of a 
 Brownian motion. We will conjecture that on an approximation of a simply c
 onnected planar domain our pseudo-metric converges to the conformal invari
 ant metric on CLE4 loops given by the CLE4 growth process. Moreover\, iden
 tities on the cable graph lead by convergence to some explicit distributio
 ns for some local sets of two-dimensional continuum GFF\, not only on a si
 mply connected domain of C but on general Riemann surfaces.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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