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CATEGORIES:Probability
SUMMARY:Local time at zero metric associated to a GFF on a
cable graph. - Titus Lupu (ETH Zurich)
DTSTART;TZID=Europe/London:20161011T163000
DTEND;TZID=Europe/London:20161011T173000
UID:TALK67741AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/67741
DESCRIPTION:We will consider an electrical network and replace
the discrete edges by continuous lines of appropr
iate length. This is a cable graph. The discrete G
aussian Free Field (GFF) on the network can be int
erpolated to a continuous process on the cable gra
ph and which satisfies the Markov property. This i
s the cable GFF. We will consider a pseudo-metric
on the cable graph related to the local time at ze
ro of the cable GFF. We will compute some universa
l explicit laws for this metric and show a general
ization on the cable graph of Lévy’s theorem for t
he local time at zero of a Brownian motion. We wil
l conjecture that on an approximation of a simply
connected planar domain our pseudo-metric converge
s to the conformal invariant metric on CLE4 loops
given by the CLE4 growth process. Moreover\, ident
ities on the cable graph lead by convergence to so
me explicit distributions for some local sets of t
wo-dimensional continuum GFF\, not only on a simpl
y connected domain of C but on general Riemann sur
faces.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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