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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Edge reinforced random walks\, Vertex reinforced j
ump process\, and the SuSy hyperbolic sigma model
(II) - Tarres\, P (University of Oxford)
DTSTART;TZID=Europe/London:20120919T093000
DTEND;TZID=Europe/London:20120919T101000
UID:TALK39907AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39907
DESCRIPTION:Edge-reinforced random walk (ERRW)\, introduced by
Coppersmith and Diaconis in 1986\, is a random pr
ocess which takes values in the vertex set of a gr
aph G\, and is more likely to cross edges it has v
isited before. We show that it can be represented
in terms of a Vertex-reinforced jump process (VRJP
) with independent gamma conductances: the VRJP wa
s conceived by Werner and first studied by Davis a
nd Volkov (2002\,2004)\, and is a continuous-time
process favouring sites with more local time.\n\nT
hen we prove that the VRJP is a mixture of time-ch
anged Markov jump processes and calculate the mixi
ng measure\, which we interpret as a marginal of t
he supersymmetric hyperbolic sigma model introduce
d by Disertori\, Spencer and Zirnbauer.\n\nThis en
ables us to deduce that VRJP and ERRW are strongly
recurrent in any dimension for large reinforcemen
t (in fact\, on graphs of bounded degree)\, using
a localisation result of Disertori and Spencer (20
10).\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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