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CATEGORIES:Probability
SUMMARY:Recurrence of the vertex-reinforced jump process i
n two dimensions - Tyler Helmuth (Bristol)
DTSTART;TZID=Europe/London:20180306T161500
DTEND;TZID=Europe/London:20180306T171500
UID:TALK97876AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/97876
DESCRIPTION: The vertex-reinforced jump process (VRJP) is a li
nearly reinforced random walk in continuous time.
Reinforcing means that the VRJP prefers to jump to
vertices it has previously visited\; the strength
of the reinforcement is a parameter of the model.
\n\nSabot and Tarres have shown that the VRJP is r
elated to a model known as the H22 supersymmetric
hyperbolic spin model\, which originated in the st
udy of random band matrices. By making use of resu
lts for the H22 model they proved the VRJP is recu
rrent for sufficiently strong reinforcement. I wil
l present a new and direct connection between the
VRJP and hyperbolic spin models (both supersymmetr
ic and classical)\, and show how this connection c
an be used to prove that the VRJP is recurrent in
two dimensions for all reinforcement strengths.\n\
nThis talk is about joint work with R. Bauerschmid
t and A. Swan.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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