Jess Jay

Interacting Particle Systems and Jacobi Style Identities

The study of nearest neighbour interacting particle systems on the integer line has a rich history. Although most work in this area concerns the case of translation invariant measures, it can be fruitful to look beyond this case. In 2018, Balazs and Bowen considered product blocking measures for ASEP and ZRP. By relating the two they found a probabilistic proof of the Jacobi triple product identity, a well-known classical identity appearing throughout Mathematics and Physics.

Naturally, one asks if other systems give rise to identities with combinatorial significance, via their blocking measures. In this talk we parameterise such a family and show that it gives rise to new 3 variable combinatorial identities.

(This is joint work with M. Balazs and D. Fretwell).