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SUMMARY:Recurrence of the vertex-reinforced jump process in two dimensions
  - Tyler Helmuth (Bristol)
DTSTART:20180306T161500Z
DTEND:20180306T171500Z
UID:TALK97876@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION: The vertex-reinforced jump process (VRJP) is a linearly reinf
 orced random walk in continuous time. Reinforcing means that the VRJP pref
 ers to jump to vertices it has previously visited\; the strength of the re
 inforcement is a parameter of the model.\n\nSabot and Tarres have shown th
 at the VRJP is related to a model known as the H22 supersymmetric hyperbol
 ic spin model\, which originated in the study of random band matrices. By 
 making use of results for the H22 model they proved the VRJP is recurrent 
 for sufficiently strong reinforcement. I will present a new and direct con
 nection between the VRJP and hyperbolic spin models (both supersymmetric a
 nd classical)\, and show how this connection can be used to prove that the
  VRJP is recurrent in two dimensions for all reinforcement strengths.\n\nT
 his talk is about joint work with R. Bauerschmidt and A. Swan.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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