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CATEGORIES:Probability
SUMMARY:Collision of random walks - Perla Sousi (Cambridge
)
DTSTART;TZID=Europe/London:20100202T163000
DTEND;TZID=Europe/London:20100202T173000
UID:TALK23130AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/23130
DESCRIPTION:Regarding his 1920 paper proving recurrence of ran
dom walks in Z^2^\, Polya wrote that his motivatio
n was to determine whether 2 independent random wa
lks 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 differ
ences. Perhaps surprisingly\, however\, there exis
t graphs G where a single random walk is recurrent
\, yet G has the *finite collision property* : two
independent random walks in G collide only finite
ly many times almost surely. Some examples were co
nstructed by Krishnapur and Peres (2004)\, who ask
ed whether critical Galton-Watson trees conditione
d on nonextinction also have this property. In thi
s talk I will answer this question as part of a sy
stematic study of the finite collision property. I
n particular\, for two classes of graphs\, wedge c
ombs and spherically symmetric trees\, we exhibit
a phase transition for the finite collision proper
ty when growth parameters are varied. I will state
the main theorems and give some ideas of the proo
fs. This is joint work with Martin Barlow and Yuva
l Peres.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Berestycki
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