Jacobi triple product via the exclusion process

I will give a brief overview of very simple, hence maybe less investigated structures in interacting particle systems: reversible product blocking measures. These turn out to be more general than most people would think, in particular asymmetric simple exclusion and nearest-neighbour asymmetric zero range processes both enjoy them. But a careful look reveals that these two are really the same process. Exploitation of this fact gives rise to the Jacobi triple product formula - an identity previously known from algebra, combinatorics and number theory. I will show you the main steps of deriving it from pure probability this time, and I hope to surprise my audience as much as we got surprised when this identity first popped up in our notebooks.