Mermin-Wagner Theorem for vertex-reinforced jump process
The vertex-reinforced jump process (VJRP) is a random walk that prefers to jump to vertices visited in the past. Hyperbolic sigma models are
spin models where the spins take values in a hyperbolic space. I will explain a relation between the VRJP and hyperbolic sigma models which
parallels that between the simple random walk and the Gaussian free field. I will further show a Mermin-Wagner Theorem for hyperbolic sigma
models which implies that the VRJP is recurrent in two dimensions.

This is joint work with Tyler Helmuth and Andrew Swan.
Date: 4 June 2018, 12:00 (Monday, 7th week, Trinity 2018)
Venue: Mathematical Institute, Woodstock Road OX2 6GG
Venue Details: L4
Speaker: Roland Bauerschmidt (Statslab, University of Cambridge)
Organising department: Department of Statistics
Organisers: Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)
Part of: Probability seminar
Booking required?: Not required
Audience: Public
Editor: Christina Goldschmidt