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SUMMARY:Sharpness of the phase transition for random-cluster and Potts mod
 el via decision trees - Aran Raoufi (Geneva)
DTSTART:20170502T151500Z
DTEND:20170502T161500Z
UID:TALK72415@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We prove that the phase transition of random-cluster and Potts
  models on any transitive graph is sharp. That is\, we show that for $p < 
 p_c$\, the probability that the origin is connected by an open path to dis
 tance $n$ decays exponentially fast in $n$. This would also imply the shar
 pness of phase transition for the Potts model.\nA main ingredient of the p
 roof comes from the theory of decision trees. An inequality on decision tr
 ees on monotonic measures is obtained which generalises the OSSS inequalit
 y on product spaces.\nThis talk is based on works with H. Duminil-Copin an
 d V. Tassion.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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