Workshop "Gauge theories and spin systems: Yang-Mills theory, continuous symmetry, and disorder"

Continuous Symmetries and the Arboreal Gas

Jul 28, 2025, 9:20 AM

1h

Poppelsdorfer Allee 45, 1. EG, Lecture room (HIM)

Scheduled Talks

Speaker

Mr Tyler Helmuth (University of Durham)

Description

I will begin by reviewing (some of) what is known and conjectured about $O(N)$ spin models. This is meant to motivate the study of the arboreal gas, a combinatorial probability model of random forests. Surprisingly, the arboreal gas has a hidden continuous symmetry similar to that of an $O(N)$ model. As a consequence one expects it to behave similarly. This turns out to be correct: several important rigorous results for $O(N)$ spin models have been shown to hold for the arboreal gas. The combinatorial nature of the arboreal gas suggests it may be a simpler setting than the $O(N)$ models for investigating open conjectures.