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CATEGORIES:Optimization and Incentives Seminar
SUMMARY:Collision of random walks - Perla Sousi\, Statisti
cal Laboratory\, University of Cambridge.
DTSTART;TZID=Europe/London:20100202T163000
DTEND;TZID=Europe/London:20100202T173000
UID:TALK23151AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23151
DESCRIPTION:Regarding his 1920 paper proving recurrence of ran
dom walks in Z2\, Polya wrote that his motivation
was to determine whether 2 independent random walk
s in Z2 meet infinitely often. Of course\, in this
case\, the problem reduces to the recurrence of a
single random walk in Z2\, by taking differences.
Perhaps surprisingly\, however\, there exist grap
hs G where a single random walk is recurrent\, yet
G has the finite collision property : two indepen
dent random walks in G collide only finitely many
times almost surely. Some examples were constructe
d by Krishnapur and Peres (2004)\, who asked wheth
er critical Galton-Watson trees conditioned on non
extinction also have this property. In this talk I
will answer this question as part of a systematic
study of the finite collision property. In partic
ular\, for two classes of graphs\, wedge combs and
spherically symmetric trees\, we exhibit a phase
transition for the finite collision property when
growth parameters are varied. I will state the mai
n theorems and give some ideas of the proofs. This
is joint work with Martin Barlow and Yuval Peres.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Neil Walton
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