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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Recurrence of planar graph limits - Gurel Gurevich
\, O (Hebrew University of Jerusalem)
DTSTART;TZID=Europe/London:20150422T153000
DTEND;TZID=Europe/London:20150422T163000
UID:TALK59060AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/59060
DESCRIPTION:Co-author: Asaf Nacmias (Tel Aviv University) \n\n
What does a random planar triangulation on n verti
ces looks like? More precisely\, what does the loc
al neighbourhood of a fixed vertex in such a trian
gulation looks like? When n goes to infinity\, the
resulting object is a random rooted graph called
the Uniform Infinite Planar Triangulation (UIPT).
Angel\, Benjamini and Schramm conjectured that the
UIPT and similar objects are recurrent\, that is\
, a simple random walk on the UIPT returns to its
starting vertex almost surely. In a joint work wit
h Asaf Nachmias\, we prove this conjecture. The pr
oof uses the electrical network theory of random w
alks and the celebrated Koebe-Andreev-Thurston cir
cle packing theorem. We will give an outline of th
e proof and explain the connection between the cir
cle packing of a graph and the behaviour of a rand
om walk on that graph.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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