Exact solutions to multi-species exclusion processes
Evan WIlliams Theatre
Peter Hall Building
Exclusion processes have been default models for transportation phenomenona. One fundamental issue is to compute exact formulae for relevant observables analytically, and a large number of results have been reported for single-species systems. In this talk, we focus on multi-species exclusion processes, and propose two approaches for exact solutions. The first one is due to duality, which is defined by a function that co-varies in time with respect to the evolution of two processes. We will propose a systematic method to construct dualities between the multi-species asymmetric exclusion processes (mASEP), via solutions of the deformed Knizhnik-Zamolodchikov equation. The second approach is through solving the master equation. We consider an exclusion process with two species of particles: the AHR (Arndt-Heinzl-Rittenberg) model, and will give a full derivation of its Green's function as well as its joint current distributions. We will also present results on its long time behaviour with step type initial conditions, and derive non-Gaussian distribution functions that also appear in the statistics of eigenvalues of random matrices.
Zeying Chen, The University of Melbourne