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SUMMARY:The geometry of random walk isomorphism theorems - Andrew Swan (Un
 iversity of Cambridge)
DTSTART:20190515T150000Z
DTEND:20190515T160000Z
UID:TALK125200@talks.cam.ac.uk
CONTACT:59181
DESCRIPTION:The classical random walk isomorphism theorems are a collectio
 n of bizarre distributional identities which relate observables of a simpl
 e random walk + its local time field to associated observables of a Gaussi
 an Free Field\, a spin system taking values in Euclidean space. In this ta
 lk\, I will present a new and very simple framework for constructing these
  isomorphism theorems\, where they are realised in terms of the continuous
  symmetries of the GFF. The key advantage of this framework is that it doe
 s not rely on explicit Euclidean/Gaussian computations\, and as a result\,
  allows us to extend the classical results to hyperbolic and spherical geo
 metries. Here\, the corresponding random walks are no longer Markovian: th
 ey are the vertex-reinforced and vertex-diminished jump processes. I will 
 also discuss the supersymmetric versions of these spin systems\, and prese
 nt some simple applications of the results.
LOCATION:MR14\, Centre for Mathematical Sciences
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