Fluctuation Properties of the TASEP with Periodic Initial Configuration
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- Borodin, A., Ferrari, P.L., Prähofer, M. et al. J Stat Phys (2007) 129: 1055. doi:10.1007/s10955-007-9383-0
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We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us (Sasamoto in J. Phys. A 38:L549–L556, 2005) and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.