Spin systems and some natural questions in probability
It has long been known that many interesting questions in
probability have a formulation in the language of spin systems. However, it
has been only rather recently that the methods developed for spin systems
were applied to finally obtain answers to some of these questions. In this
talk, I will discuss three such questions, about the weakly self-avoiding
walk, the vertex reinforced jump process, and random band matrices. I will
then show the audience some technical lemmas that are at
the heart of the analysis of spin systems.