Modul: MAT971 Stochastische Prozesse

## Spin systems, isomorphism theorems, and random walks

Dr. Tyler Helmuth talk

**Date:** 27.02.19 **Time:** 17.15 - 19.00 **Room:** Y27H12

The classical isomorphism theorems are distributional identities that relate the local times of simple random walk to the square of the Gaussian free field (GFF). It is possible to see these relations as a consequence of the continuous translation symmetry of the GFF, and by using similar ideas it is possible to derive isomorphism theorems that relate the vertex-reinforced jump process to hyperbolic spin systems. I will explain how this works, and how the resulting identities can be used to prove the recurrence of the vertex-reinforced jump process on the two-dimensional square lattice.