Current fluctuations for totally asymmetric exclusion on the relaxation scale

Abstract

The fluctuations of the current for the one-dimensional totally asymmetric exclusion process with $L$ sites are studied in the relaxation regime of times $T\sim L^{3/2}$. Using Bethe ansatz for the periodic system with an evolution conditioned on special initial and final states, the Fourier transform of the probability distribution of the fluctuations is calculated exactly in the thermodynamic limit $L\to \infty$ with finite density of particles. It is found to be equal to a sum over discrete realizations of a scalar field in a linear potential with coupling constant equal to the rescaled time $T/L^{3/2}$.

arXiv comment9 pages, 2 figures

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• Integral formulas of ASEP and $q$-TAZRP on a ring
• Current fluctuations and large deviations for periodic TASEP on the relaxation scale
• Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process
• KPZ fluctuations in finite volume
• Current statistics in the q-boson zero range process