Asymmetric simple exclusion process and modified random matrix ensembles Original Research Article

We study the fluctuation properties of the asymmetric simple exclusion process (ASEP) on an infinite one-dimensional lattice. When N particles are initially situated in the negative region with a uniform density image, Johansson showed the equivalence of the current fluctuation of ASEP and the largest eigenvalue distribution of random matrices. We extend Johanssonʹs formula and derive modified ensembles of random matrices, corresponding to general ASEP initial conditions. Taking the scaling limit, we find that a phase change of the asymptotic current fluctuation occurs at a critical position.