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CATEGORIES:Probability
SUMMARY: Edge reinforced random walks\, Vertex reinforced
jump process\, and the SuSy hyperbolic sigma model
. - Pierre Tarres (Oxford)
DTSTART;TZID=Europe/London:20120515T160000
DTEND;TZID=Europe/London:20120515T170000
UID:TALK37960AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/37960
DESCRIPTION:Edge-reinforced random walk (ERRW)\, introduced by
Coppersmith and Diaconis\nin 1986\, is a random p
rocess which takes values in the vertex set of a g
raph\nG\, and is more likely to cross edges it has
visited\nbefore. We show that it can be represent
ed in terms of a Vertex-reinforced\njump process (
VRJP) with independent gamma conductances: the VRJ
P was\nconceived by Werner and first studied by Da
vis and Volkov (2002\,2004)\, and\nis a continuous
-time process favouring sites with more local time
.\n\nThen we prove that the VRJP is a mixture of t
ime-changed Markov\njump processes and calculate t
he mixing measure\, which we interpret as\na margi
nal of the supersymmetric hyperbolic sigma model i
ntroduced\nby Disertori\, Spencer and Zirnbauer (2
010).\n\nThis enables us to deduce that VRJP and E
RRW are positive recurrent on\ngraphs of bounded d
egree for large reinforcement\, and that VRJP is t
ransient\nin dimension greater than or equal to 3
for small reinforcment\, using the\nprevious resul
ts of Disertori and Spencer and Zirnbauer.\n\n(Joi
nt work with Christophe Sabot)\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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