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

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...

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Veröffentlicht in:	arXiv.org 2006-11
Hauptverfasser:	Borodin, Alexei, Ferrari, Patrik L, Prähofer, Michael
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Sprache:	eng
Schlagworte:	Growth models Initial conditions Variation
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description	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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title	Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process
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