### Abstract of "Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_{1} process"

with Alexei Borodin and Michael PrÃ¤hofer.

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 **Z**, 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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arXiv: math-ph/0611071