Fluctuation properties of the TASEP with periodic initial configuration

Alexei Borodin, Patrik L. Ferrari, Michael Prähofer, Tomohiro Sasamoto

Published 2006-08-25, updated 2006-12-14Version 3

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 and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.