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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
(I) - Sabot\, C (Universit Claude Bernard Lyon 1)
DTSTART;TZID=Europe/London:20120918T162000
DTEND;TZID=Europe/London:20120918T170000
UID:TALK39843AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39843
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

\nThen we prove that the VRJP is a mixture of
time-changed Markov jump processes and calculate t
he mixing measure\, which we interpret as a margin
al of the supersymmetric hyperbolic sigma model in
troduced by Disertori\, Spencer and Zirnbauer.\n\nThis enables us to deduce that VRJP and ERR
W are strongly recurrent in any dimension for larg
e reinforcement (in fact\, on graphs of bounded de
gree)\, using a localisation result of Disertori a
nd Spencer (2010).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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