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SUMMARY:The uniform spanning forest of planar graphs - Nachmias\, A (Tel A
 viv University)
DTSTART:20150423T080000Z
DTEND:20150423T090000Z
UID:TALK59134@talks.cam.ac.uk
CONTACT:42082
DESCRIPTION:The free uniform spanning forest (FUSF) of an infinite graph G
  is obtained as the weak limit of the law of a uniform spanning tree on G_
 n\, where G_n is a finite exhaustion of G. It is easy to see that the FUSF
  is supported on spanning graphs of G with no cycles\, but it need not be 
 connected. Indeed\, a classical result of Pemantle ('91) asserts that when
  G=Z^d\, the FUSF is almost surely a connected tree if and only if d=1\,2\
 ,3\,4.\n\nIn this talk we will show that if G is a plane graph with bounde
 d degrees\, then the FUSF is almost surely connected\, answering a questio
 n of Benjamini\, Lyons\, Peres and Schramm ('01). An essential part of the
  proof is the circle packing theorem.\n\nJoint work with Tom Hutchcroft.\n
LOCATION:Seminar Room 1\, Newton Institute
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