Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles

Details Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles

2004-05-14

arxiv.org/abs/cond-mat/0405321v1

Nucl. Phys. B699 (2004) 487

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 18 pages, no figure

Scientific paper

10.1016/j.nuclphysb.2004.08.016

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 $\rho_-=1$, Johansson showed the equivalence of the current fluctuation of ASEP and the largest eigenvalue distribution of random matrices. We extend Johansson's 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.

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