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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:The geometry of random walk isomorphism theorems -
Andrew Swan (University of Cambridge)
DTSTART;TZID=Europe/London:20190515T160000
DTEND;TZID=Europe/London:20190515T170000
UID:TALK125200AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/125200
DESCRIPTION:The classical random walk isomorphism theorems are
a collection of bizarre distributional identities
which relate observables of a simple random walk
+ its local time field to associated observables o
f a Gaussian Free Field\, a spin system taking val
ues in Euclidean space. In this talk\, I will pres
ent a new and very simple framework for constructi
ng these isomorphism theorems\, where they are rea
lised in terms of the continuous symmetries of the
GFF. The key advantage of this framework is that
it does not rely on explicit Euclidean/Gaussian co
mputations\, and as a result\, allows us to extend
the classical results to hyperbolic and spherical
geometries. Here\, the corresponding random walks
are no longer Markovian: they are the vertex-rein
forced and vertex-diminished jump processes. I wil
l also discuss the supersymmetric versions of thes
e spin systems\, and present some simple applicati
ons of the results.
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:
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