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

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.

45 pages, 7 figures, LaTeX

References in corpus (6)

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Cited by in corpus (5)

• Fluctuation properties of the TASEP with periodic initial configuration
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process
• Determinantal Expressions in Multi-Species TASEP