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Finite-Time Current Probabilities in the Asymmetric Exclusion Process on a Ring

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Abstract

We calculate the time-dependent probability distribution of current through a selected bond in the totally asymmetric exclusion process with periodic boundary conditions. We derive a general formula for the probability that the integrated current exceeds a given value N at the moment of time t. The formula is written in a form of a contour integral of a determinant of a Toeplitz matrix. Transforming the determinant expression, we obtain a generalization of the known formula derived by Johansson for the infinite one-dimensional lattice. To check the general formula, we consider the specific case corresponding to the probability of a minimal non-zero current. For this case we get an explicit analytical expression and analyze its asymptotics.

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Authors and Affiliations

  1. Dublin Institute for Advanced Studies, School of Theoretical Physics, 10 Burlington Road, Dublin, 4, Ireland

    T. C. Dorlas

  2. Joint Institute for Nuclear Research, Laboratory of Theoretical Physics, Dubna, Russia

    V. B. Priezzhev

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  1. T. C. Dorlas
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  2. V. B. Priezzhev
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Correspondence to T. C. Dorlas.

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Dorlas, T.C., Priezzhev, V.B. Finite-Time Current Probabilities in the Asymmetric Exclusion Process on a Ring. J Stat Phys 129, 787–805 (2007). https://doi.org/10.1007/s10955-007-9406-x

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  • DOI: https://doi.org/10.1007/s10955-007-9406-x

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