Spin systems with hyperbolic symmetry: a survey
Roland Bauerschmidt
DPMMS, University of Cambridge, Cambridge CB3 0WB, UKTyler Helmuth
Mathematical Sciences, Durham University, Durham DH1 3LE, UK
![Spin systems with hyperbolic symmetry: a survey cover](/_next/image?url=https%3A%2F%2Fcontent.preview.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-277.png&w=3840&q=90)
Download Chapter PDF
This book chapter is published open access.
Abstract
Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal–insulator transition, and were subsequently found to exactly describe probabilistic models of linearly reinforced walks and random forests. In this survey we introduce these models, discuss their origins and main features, some existing tools available for their study, recent probabilistic results, and relations to other well-studied probabilistic models. Along the way we discuss some of the many open questions that remain.