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 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. 
Alexei Borodin (1), Patrik L. Ferrari (2), Michael Pr\"ahofer (2) ((1)   Caltech, (2) TU-Muenchen)