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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The uniform spanning forest of planar graphs - Nac
hmias\, A (Tel Aviv University)
DTSTART;TZID=Europe/London:20150423T090000
DTEND;TZID=Europe/London:20150423T100000
UID:TALK59134AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/59134
DESCRIPTION:The free uniform spanning forest (FUSF) of an infi
nite 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 tha
t the FUSF is supported on spanning graphs of G wi
th no cycles\, but it need not be connected. Indee
d\, a classical result of Pemantle ('91) asserts t
hat when G=Z^d\, the FUSF is almost surely a conne
cted 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
bounded degrees\, then the FUSF is almost surely c
onnected\, answering a question of Benjamini\, Lyo
ns\, 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
CONTACT:
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