Exact solutions to multispecies exclusion processes
Seminar/Forum
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 singlespecies systems. In this talk, we focus on multispecies exclusion processes, and propose two approaches for exact solutions. The first one is due to duality, which is defined by a function that covaries in time with respect to the evolution of two processes. We will propose a systematic method to construct dualities between the multispecies asymmetric exclusion processes (mASEP), via solutions of the deformed KnizhnikZamolodchikov equation. The second approach is through solving the master equation. We consider an exclusion process with two species of particles: the AHR (ArndtHeinzlRittenberg) 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 nonGaussian distribution functions that also appear in the statistics of eigenvalues of random matrices.
Presenter

Zeying Chen, The University of Melbourne