B. Derrida, J. L. Lebowitz
Exact large deviation function in the asymmetric exclusion
process 
(24K, RevTeX)

ABSTRACT.  By an extension of the Bethe ansatz method used by Gwa and Spohn, we
obtain an exact expression for the large deviation function of the
time averaged current for the fully asymmetric exclusion process in a
ring containing $N$ sites and $p$ particles.  Using this expression we
easily recover the exact diffusion constant obtained earlier and
calculate as well some higher cumulants.  The distribution of the
deviation $y$ of the average current is, in the limit $N \to \infty$,
skew and decays like $\exp - (A y^{5/2})$ for $y \to + \infty$ and
$\exp - (A' |y|^{3/2})$ for $y \to -\infty$.  Surprisingly, the large
deviation function has an expression very similar to the pressure (as
a function of the density) of an ideal Bose or Fermi gas in $3d$.