Determinant solution for the Totally Asymmetric Exclusion Process with parallel update

Abstract

We consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The non-stationary solution of the master equation for the infinite 1D lattice is obtained in a determinant form. Using a modified combinatorial treatment of the Bethe ansatz, we give an alternative derivation of the resulting determinant expression.

34 pages, 5 figures, final version

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Cited by in corpus (24)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
• Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
• On integrability of zero-range chipping models with factorized steady state
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz
• Determinantal transition kernels for some interacting particles on the line
• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process
• Determinant solution for the Totally Asymmetric Exclusion Process with parallel update II. Ring geometry
• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Emergence of jams in the generalized totally asymmetric simple exclusion process
• Determinant representation for some transition probabilities in the TASEP with second class particles
• The totally asymmetric exclusion process with generalized update
• Multi-point distribution of periodic TASEP
• TASEP and generalizations: Method for exact solution
• Integral formulas of ASEP and $q$-TAZRP on a ring
• On the blockage problem and the non-analyticity of the current for the parallel TASEP on a ring
• Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process
• Generalized Green Functions and current correlations in the TASEP
• KPZ fluctuations in finite volume
• The KPZ fixed point for discrete time TASEPs
• Multi-point distribution of discrete time periodic TASEP