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Fluctuation properties of the TASEP with periodic initial configuration

A. Borodin, P. L. Ferrari, M. Prähofer, T. Sasamoto

J. Stat. Phys. 129, 1055-1080 (2007)

DOI: 10.1007/s10955-007-9383-0 Pfeil
*arXiv.org*: math-ph/0608056 Pfeil
*MathSciNet*: MR2363389 Pfeil

Abstract: We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.