08May 2019

Seminar in probability theory: Roland Bauerschmidt (University of Cambridge)

The geometry of random walk isomorphisms

The classical random walk isomorphism theorems relate the local time of a random walk to the square of a Gaussian free field. I will present non-Gaussian versions of these theorems, relating hyperbolic and hemispherical sigma models (and their supersymmetric versions) to non-Markovian random walks interacting through their local time. Applications include a short proof of the Sabot-Tarres limiting formula for the vertex-reinforced jump process (VRJP) and a Mermin-Wagner theorem for hyperbolic sigma models and the VRJP. This is joint work with Tyler Helmuth and Andrew Swan.

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