# Shock fluctuations for the asymmetric simple exclusion process

## P.A. Ferrari, L. R. Fontes

We consider the one dimensional nearest neighbors asymmetric simple exclusion process with rates $q$ and $p$ for left and right jumps respectively; $q<p$. Ferrari, Kipnis and Saada (1991) have shown that if the initial measure is $\nurl$, a product measure with densities $\rho$ and $\la$ to the left and right of the origin respectively, $\rho<\la$, then there exists a (microscopic) shock for the system. A shock is a random position $X_t$ such that the system as seen from this position at time $t$ has asymptotic product distributions with densities $\rho$ and $\la$ to the left and right of the origin respectively, uniformly in $t$. We compute the diffusion coefficient of the shock $D=\limt t^{-1}(E(X_t)^2 - (EX_t)^2)$ and find $D=(p-q)(\la-\rho)^{-1} (\rho(1-\rho)+\la(1-\la))$ as conjectured by Spohn (1991). We show that in the scale $\sqrt t$ the position of $X_t$ is determined by the initial distribution of particles in a region of lenght proportional to $t$. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities $\rho$ and $\la$. This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration. </plaintext> <hr> <address></address> <!-- hhmts start --> Last modified: Fri Dec 6 18:12:32 EDT 1996 <!-- hhmts end --> </body> </html>