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Fluctuation properties of the TASEP with periodic initial configuration. (English) Zbl 1136.82028
Summary: 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 [T. Sasamoto, Spatial correlations of the 1D KPZ surface on a flat substrate, J. Phys. A 38, L549–L556 (2005), doi:10.1088/0305-4470/38/33/L01)] and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.

MSC:
82C22 Interacting particle systems in time-dependent statistical mechanics
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82C43 Time-dependent percolation in statistical mechanics
15B52 Random matrices (algebraic aspects)
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