CANCELLED – Richard P. Stanley Seminar in Combinatorics: Colored Interacting Particle Systems on the Ring: Stationary Measures from Yang–Baxter Equation
SEMINARS, HARVARD-MIT COMBINATORICS
Matthew Nicoletti - MIT
Seminar CANCELLED due to speaker illness. Will be rescheduled at a different date
Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or multi-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.
For more info, see https://math.mit.edu/combin/