The asymmetric Exclusion Process and Brownian Excursions
B. Derrida, C. Enaud, J. L. Lebowitz
TL;DR
This paper demonstrates that in the maximal current phase of the 1D TASEP, density fluctuations are governed by Brownian excursions, with numerical evidence suggesting this applies broadly to similar driven systems.
Contribution
It provides an exact analytical link between TASEP density fluctuations and Brownian excursions, extending understanding of non-Gaussian fluctuation behavior in driven systems.
Findings
Density fluctuations described by Brownian excursions
Exact calculation for TASEP in maximal current phase
Numerical simulations support broader applicability
Abstract
We consider the totally asymmetric exclusion process (TASEP) in one dimension in its maximal current phase. We show, by an exact calculation, that the non-Gaussian part of the fluctuations of density can be described in terms of the statistical properties of a Brownian excursion. Numerical simulations indicate that the description in terms of a Brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase.
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