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SUMMARY:Collision of random walks - Perla Sousi\, Statistical Laboratory\,
  University of Cambridge.
DTSTART:20100202T163000Z
DTEND:20100202T173000Z
UID:TALK23151@talks.cam.ac.uk
CONTACT:Neil Walton
DESCRIPTION:Regarding his 1920 paper proving recurrence of random walks in
  Z2\, Polya wrote that his motivation was to determine whether 2 independe
 nt random walks in Z2 meet infinitely often. Of course\, in this case\, th
 e problem reduces to the recurrence of a single random walk in Z2\, by tak
 ing differences. Perhaps surprisingly\, however\, there exist graphs G whe
 re a single random walk is recurrent\, yet G has the finite collision prop
 erty : two independent random walks in G collide only finitely many times 
 almost surely. Some examples were constructed by Krishnapur and Peres (200
 4)\, who asked whether critical Galton-Watson trees conditioned on nonexti
 nction also have this property. In this talk I will answer this question a
 s part of a systematic study of the finite collision property. In particul
 ar\, for two classes of graphs\, wedge combs and spherically symmetric tre
 es\, we exhibit a phase transition for the finite collision property when 
 growth parameters are varied. I will state the main theorems and give some
  ideas of the proofs. This is joint work with Martin Barlow and Yuval Pere
 s.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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