# Transition probabilities and asymptotics for integrable two-species stochastic processes

I will discuss exact, multiple integral formulas for the transition probability (Green's function) of two different integrable two-species stochastic particle models: the Arndt-Heinzel-Rittenberg (AHR) model and the 2-TASEP whose generator is the $q\rightarrow 0$ limit of the R-matrix related to $U_q(sl(3))$. We derive closed form formulas for total crossing probabilities. In the case of the AHR I will sketch how an asymptotic analysis of these expressions leads to a rigorous derivation of universal hydrodynamic probability distribution functions. The latter lie in the KPZ universality class and are related to distributions from random matrix theory.

This is work in collaboration with Zeying Chen, Iori Hiki, William Mead, Masato Usui, Michael Wheeler and Tomohiro Sasamoto.

Relevant papers: Phys. Rev. Lett. 120, 240601 (2018), A paper on 2-TASEP is in final stages of preparation

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