Journal Article


V. B. Priezzhev
T. C. Dorlas



probabilities expression current asymmetric boundary conditions exclusion integrated probability distribution

Finite-Time Current Probabilities in the Asymmetric Exclusion Process on a Ring (2007)

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.
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Full list of authors on original publication

V. B. Priezzhev, T. C. Dorlas

Experts in our system

T. C. Dorlas
Total Publications: 44