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SUMMARY:Reinforced Random Walk and a Supersymmetric Spin System on the Tre
 e - Peter Wildemann (Cambridge)
DTSTART:20240528T143000Z
DTEND:20240528T153000Z
UID:TALK217423@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:Motivated by predictions about the Anderson transition\, we\ns
 tudy two distinct but related models on regular tree graphs: The\nvertex-r
 einforced jump process (VRJP)\, a random walk preferring to\njump to previ
 ously visited sites\, and the H^{2|2}-model\, a lattice\nspin system whose
  spins take values in a supersymmetric extension of\nthe hyperbolic plane.
  Both models undergo a phase transition\, and our\nwork provides detailed 
 information about the supercritical phase up to\nthe critical point: We sh
 ow that their order parameter has an\nessential singularity as one approac
 hes the critical point\, in\ncontrast to algebraic divergences typically e
 xpected for statistical\nmechanics models. Moreover\, we identify a previo
 usly unexpected\nmultifractal intermediate regime in the supercritical pha
 se. This talk\nis based on arxiv:2309.01221 and is joint work with R??my P
 oudevigne.\n
LOCATION:MR12
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