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

References in corpus (4)

• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• A determinantal formula for the GOE Tracy-Widom distribution
• Bethe ansatz solution of discrete time stochastic processes with fully parallel update
• Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates

Cited by in corpus (6)

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• 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