Fluctuation properties of the TASEP with periodic initial configuration

Abstract

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.

33 pages, 4 figure, LaTeX; We added several references to the general framework and techniques used

References in corpus (5)

• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• A determinantal formula for the GOE Tracy-Widom distribution
• Universality for mathematical and physical systems
• Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates

Cited by in corpus (10)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Slow decorrelations in KPZ growth
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• Determinantal transition kernels for some interacting particles on the line
• The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process
• Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model
• From Vicious Walkers to TASEP
• Large time asymptotics of growth models on space-like paths I: PushASEP