Richard P. Stanley Seminar in Combinatorics: Matthew Nicoletti (MIT)

Harvard Science Center 232

Speaker: Matthew Nicoletti (MIT)Note: Special date, time, and location.Title: Colored Interacting Particle Systems on the Ring: Stationary Measures from Yang-Baxter EquationAbstract:Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or ulti-type) interacting particle systems, motivated by asymptotic phenomena and rich underlying algebraic and combinatorial structures (such as nonsymmetric Macdonald polynomials).In this work, we present a unified approach to constructing stationary measures for several colored particle systems on the ring and the line, including (1) the Asymmetric Simple Exclusion Process (mASEP); (2) the q-deformed Totally Asymmetric Zero Range Process (TAZRP) also known as the q-Boson particle system; (3) the q-deformed Pushing Totally Asymmetric Simple Exclusion Process (q-PushTASEP). Our method is based on integrable stochastic vertex models and the Yang--Baxter equation. We express the stationary measures as partition functions of new "queue vertex models'' on the cylinder. The stationarity property is a direct consequence of the Yang--Baxter equation. This is joint work with A. Aggarwal and L. Petrov.