PMID: 15244696Jul 13, 2004Paper

Generalized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
J G BrankovR V Shelest

Abstract

We consider the discrete-time evolution of a finite number of particles obeying the totally asymmetric exclusion process with backward-ordered update on an infinite chain. Our first result is a determinant expression for the conditional probability of finding the particles at given initial and final positions, provided that they start and finish simultaneously. The expression has the same form as the one obtained by J. Stat. Phys. 88, 427 (1997)] for the continuous-time process. Next we prove that under some sufficient conditions the determinant expression can be generalized to the case when the particles start and finish at their own times. The latter result is used to solve a nonstationary zero-range process on a finite chain with open boundaries.

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Citations

Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A E DerbyshevV B Priezzhev

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