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 6GGSee location on maps.ox**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