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 number theory and combinatorics. 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.
Jacobi triple product via the exclusion process
2019. 01. 10. 16:15
Márton Balázs (University of Bristol)