Exact formulas and asymptotics in the integrable stochastic particle models with multi species

Faculty Development Competitive Research Grant Program 2018-2020

The integrable probability named by Alexei Borodin (MIT) and Leonid Petrov (U of Virginia) a few years ago is in an interdisciplinary field that is a playground of various branches of mathematics such as analysis, representation theory, integrable system and statistical mechanics as well as probability. Various models in the integrable probability are exactly solvable in the sense thet their explicit formulas of relevant probabilities can be computed in closed forms. But, the majority of researches in this field are being performed about the models with the single species due to the complexity of computations and algebraic structures inherent in the models with multi species. In this project we want to study the models with multi species. The fundamental objects of this project can be summarized as follows.