Tagged particle in TASEP and random matrix theory

Recently, the non-Gaussian property of the current fluctuation in the totally asymmetric simple exclusion process (TASEP) has been analyzed and it turns out that the fluctuation is equivalent to the largest eigenvalue fluctuation in the random matrix model. In this presentation, we report the random matrix technique is also applicable to the position fluctuation of a tagged particle in the TASEP which is closely related to the current fluctuation. Based on the mapping to the free Fermionic system, we show that the (discretized version of) random matrix ensemble characterizes the time evolution of the tagged particle. Furthermore, the ensemble provides unified method for analyzing the tagged particle problem in the TASEP with particle-dependent hopping rate. This is the joint work with Tomohiro Sasamoto. ( ref. math-ph/0702009)