Jessica Jay

Blocking Measures for Ising Processes and Combinatorial Identities

In this talk we will study a family of Ising processes on the integer line under nearest neighbour Kawasaki dynamics. We wish to think of theses Ising processes as a generalisation of the Asymmetric Simple Exclusion Process and so we introduce a right drift to particles with positive spin (left drift to negative spin particles). For such Ising processes, with certain interaction functions, blocking measures exist.
We will see a generalisation of the exclusion – zero range correspondence by mapping the dynamics of the Ising processes to a family of interacting particle systems. This leads to combinatorial identities relating to the generating functions of over-partitions.
In this talk we will also consider long range Ising processes and see that the maps mentioned above produce reversible long-range interacting particle systems with interesting dynamics.
This is based on joint work with Ben Lees.