Prof. Jan de Gier
The University of Melbourne, Australia
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.
Thu 22 April 2021 12PM Sydney time