CANCELLED FEBRUARY 14, 2024

RESCHEDULED FOR APRIL 26, 2024

Speaker:  Matthew Nicoletti (MIT)

When:    FRIDAY, April 26, 2024, 3-4PM  (NEW DATE)

Where:   Harvard Science Center, Room 232  (Please note new location.)

                One Oxford Street

                Cambridge, MA 02138

Title:        Colored Interacting Particle Systems on the Ring: 

                 Stationary Measures from Yang-Baxter Equation

Abstract:  

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.