2007/02/28 by T. Imamura, T. Sasamoto · 3 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR #nlin.SI
paper · pdf · doi:10.1007/s10955-007-9326-9
published as J. Stat. Phys. 128 (2007) 799-846 · 48 pages, 8 figures
openalex publication_date 2007/06/14 · arxiv created 2007/07/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in TASEP with the step-type initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.