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SUMMARY:Edge reinforced random walks\, Vertex reinforced jump process\, an
 d the SuSy hyperbolic sigma model (I) - Sabot\, C (Universit Claude Bernar
 d Lyon 1)
DTSTART:20120918T152000Z
DTEND:20120918T160000Z
UID:TALK39843@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Edge-reinforced random walk (ERRW)\, introduced by Coppersmith
  and Diaconis in 1986\, is a random process which takes values in the vert
 ex set of a graph G\, and is more likely to cross edges it has visited bef
 ore. We show that it can be represented in terms of a Vertex-reinforced ju
 mp process (VRJP) with independent gamma conductances: the VRJP was concei
 ved by Werner and first studied by Davis and Volkov (2002\,2004)\, and is 
 a continuous-time process favouring sites with more local time.\n<p></p>\n
 Then we prove that the VRJP is a mixture of time-changed Markov jump proce
 sses and calculate the mixing measure\, which we interpret as a marginal o
 f the supersymmetric hyperbolic sigma model introduced by Disertori\, Spen
 cer and Zirnbauer.\n<p></p>\nThis enables us to deduce that VRJP and ERRW 
 are strongly recurrent in any dimension for large reinforcement (in fact\,
  on graphs of bounded degree)\, using a localisation result of Disertori a
 nd Spencer (2010).
LOCATION:Seminar Room 1\, Newton Institute
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