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SUMMARY:Recurrence of planar graph limits - Gurel Gurevich \, O (Hebrew Un
 iversity of Jerusalem)
DTSTART:20150422T143000Z
DTEND:20150422T153000Z
UID:TALK59140@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-author: Asaf Nacmias (Tel Aviv University) \n\nWhat does a 
 random planar triangulation on n vertices looks like? More precisely\, wha
 t does the local neighbourhood of a fixed vertex in such a triangulation l
 ooks like? When n goes to infinity\, the resulting object is a random root
 ed graph called the Uniform Infinite Planar Triangulation (UIPT). Angel\, 
 Benjamini and Schramm conjectured that the UIPT and similar objects are re
 current\, that is\, a simple random walk on the UIPT returns to its starti
 ng vertex almost surely. In a joint work with Asaf Nachmias\, we prove thi
 s conjecture. The proof uses the electrical network theory of random walks
  and the celebrated Koebe-Andreev-Thurston circle packing theorem. We will
  give an outline of the proof and explain the connection between the circl
 e packing of a graph and the behaviour of a random walk on that graph.\n
LOCATION:Seminar Room 1\, Newton Institute
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