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Fluctuations in the Discrete TASEP with Periodic Initial Configurations and the Airy1 Process

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

International Mathematics Research Papers 2007 rpm002-47 (2007)

DOI: 10.1093/imrp/rpm002 Pfeil
*arXiv.org*: math-ph/0611071 Pfeil
*MathSciNet*: MR2334008 Pfeil

Abstract: We consider the totally asymmetric simple exclusion process (TASEP) in discrete time with sequential update. The joint distribution of the positions of selected particles is expressed as a Fredholm determinant with a kernel defining a signed determinantal point process. We focus on periodic initial conditions where particles occupy dZ, d>=2. In the proper large time scaling limit, the fluctuations of particle positions are described by the Airy1 process. Interpreted as a growth model, this confirms universality of fluctuations with flat initial conditions for a discrete set of slopes.