 92116 Ferrari P.A., Fontes L.R.
 Current fluctuations for the asymmetric simple exclusion
process
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Sep 23, 92

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Abstract. We compute the diffusion coefficient of the current
of particles through a fixed point in the one dimensional nearest neighbors
asymmetric simple exclusion process
in equilibrium.
We find $D= \vert pq \vert \rho(1\rho) \vert 12\rho \vert$, where $p$ is
the rate at which the particles jump to the right, $q$ is the jump rate to the
left and $\rho$ is the density of particles. Notice that $D$ cancels if $p=q$
or $\rho = 1/2$. A law of large numbers and central limit theorems are also
proven. Analogous results are obtained for the current of particles through a
position travelling at a deterministic velocity $r$. As a corollary we get
that the equilibrium density fluctuations at time $t$ are a translation of the
fluctuations at time $0$. We also show that the current fluctuations at time
$t$ are given, in the scale $t^{1/2}$, by the initial density of particles in
an interval of length $\vert (pq)(12\rho) \vert t$. The process is
isomorphic
to a growth interface process. Our result means that the growth fluctuations
depend on the general inclination of the surface. In particular they vanish
for interfaces roughly perpendicular to the observed growth direction.
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