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SUMMARY:Collision of random walks - Perla Sousi (Cambridge)
DTSTART:20100202T163000Z
DTEND:20100202T173000Z
UID:TALK23130@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:Regarding his 1920 paper proving recurrence of random walks in
  Z^2^\, Polya wrote that his motivation was to determine whether 2 indepen
 dent random walks in Z^2^ meet infinitely often. Of course\, in this case\
 , the problem reduces to the recurrence of a single random walk in Z^2^\, 
 by taking differences. Perhaps surprisingly\, however\, there exist graphs
  G where a single random walk is recurrent\, yet G has the *finite collisi
 on property* : two independent random walks in G collide only finitely man
 y times almost surely. Some examples were constructed by Krishnapur and Pe
 res (2004)\, who asked whether critical Galton-Watson trees conditioned on
  nonextinction also have this property. In this talk I will answer this qu
 estion as part of a systematic study of the finite collision property. In 
 particular\, for two classes of graphs\, wedge combs and spherically symme
 tric trees\, we exhibit a phase transition for the finite collision proper
 ty when growth parameters are varied. I will state the main theorems and g
 ive some ideas of the proofs. This is joint work with Martin Barlow and Yu
 val Peres.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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