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

Dorlas, T. C. and Priezzhev, V. B. (2007) Finite-Time Current Probabilities in the Asymmetric Exclusion Process on a Ring. (Preprint)

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Abstract

We calculate the time-dependent probability distribution of cur-rent through a selected bond in the totally asymmetric exclusion pro-cess 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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 13:46
Last Modified: 16 Jul 2018 09:51
URI: http://dair.dias.ie/id/eprint/491

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