Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process

Details Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process

2006-11-26

arxiv.org/abs/math-ph/0611071v1

Int. Math. Res. Papers 2007, rpm002 (2007)

Physics

Mathematical Physics

45 pages, 7 figures, LaTeX

Scientific paper

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 Airy_1 process. Interpreted as a growth model, this confirms universality of fluctuations with flat initial conditions for a discrete set of slopes.

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