The asymmetric Exclusion Process and Brownian Excursions
arXiv:cond-mat/0306078 · doi:10.1023/B:JOSS.0000019833.35328.b4
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.
23 pages, 1 figure, in latex, e-mail addresses: derrida@lps.ens.fr, enaud@lps.ens.fr, lebowitz@math.rutgers.edu