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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Derrida, B., Enaud, C. & Lebowitz, J.L. The Asymmetric Exclusion Process and Brownian Excursions. Journal of Statistical Physics 115, 365–382 (2004). https://doi.org/10.1023/B:JOSS.0000019833.35328.b4
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DOI: https://doi.org/10.1023/B:JOSS.0000019833.35328.b4