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

Alexei Borodin·Patrik L. Ferrari·Michael Prähofer
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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 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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Alexei Borodin, Patrik L. Ferrari, Michael Prähofer. 2006-11-26. Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process. https://arxiv.org/abs/math-ph/0611071

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