Asymmetric simple exclusion process and modified random matrix ensembles. (English) Zbl 1123.82345
Summary: 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.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82C23 | Exactly solvable dynamic models in time-dependent statistical mechanics |
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