28/06/2023, 17:00 — 18:00 — Online
Márton Balázs, University of Bristol
Blocking measures is a combinatorial goldmine
Several asymmetric nearest-neighbour interacting particle systems possess reversible product stationary distributions called blocking measures. Whatever we ask about these a new proof of a non-trivial combinatorial identity drops out as a result. Simple exclusion's particle-hole symmetry, the number of its particles in parts of the integer line, or the exclusion-zero range correspondence each give rise to probabilistic proofs of partition identities (namely, Durfee Rectangles Identity, Euler's Identity, the q-Binomial Theorem, Jacobi Triple Product). More complicated systems beyond simple exclusion can also be studied, and these provide more involved combinatorial results, some of them completely new. I'll reveal some structures behind blocking measures, and sketch how to prove a bunch of scary-looking identities using interacting particles, hence bringing them closer to a probabilist. As a by-product the stationary location of simple exclusion's second class particles in blocking measures will also be revealed. (Joint with Dan Adams, Ross Bowen, Dan Fretwell, Jessica Jay)
See also: https://spmes.impa.br
