Asymmetric simple exclusion process and modified random matrix ensembles: Taro Nagao and Tomohiro Sasamoto

Asymmetric simple exclusion process and modified random matrix ensembles
Taro Nagao and Tomohiro Sasamoto
Nuclear Physics B
Volume 699, Issue 3, 8 November 2004, Pages 487-502.
arXiv: http://arxiv.org/abs/cond-mat/0405321

Abstract: 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.

Reflections: This paper arrives at the Johansson type results for (essentially) one-sided LPP without appealing to Young Tableaux and RSK, but rather by just using Greens functions. The Greens functions correspond to the Tracy and Widom ASEP formulas, for p=1, q=0. They derive the one-sided LPP Prahofer and Spohn conjecture from these methods. The results here are similar to the BBP results on eigenvalues of perturbed Wishart ensembles.