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We consider the one dimensional totally asymmetric simple exclusion processwith initial product distribution with densities $0 \leq \rho_0 < \rho_1 <...<\rho_n \leq 1$ in $(-\infty,c_1\ve^{-1})$,$[c_1\ve^{-1},c_2\epsilon^{-1}),...,[c_n \ve^{-1}, + \infty)$, respectively.The initial distribution has shocks (discontinuities) at $\epsilon^{-1}c_k$,k=1,...,n and we assume that in the corresponding macroscopic Burgers equationthe n shocks meet in $r^*$ at time $t^*$. The microscopic position of theshocks is represented by second class particles whose distribution in the scale$\epsilon^{-1/2}$ is shown to converge to a function of n independent Gaussianrandom variables representing the fluctuations of these particles ``just beforethe meeting''. We show that the density field at time $\ve^{-1}t^*$, in thescale $\ve^{-1/2}$ and as seen from $\ve^{-1}r^*$ converges weakly to a randommeasure with piecewise constant density as $\ve \to 0$; the points ofdiscontinuity depend on these limiting Gaussian variables. As a corollary weshow that, as $\epsilon\to 0$, the distribution of the process at site$\epsilon^{-1}r^*+\ve^{-1/2}a$ at time $\epsilon^{-1}t^*$ tends to a nontrivial convex combination of the product measures with densities $\rho_k$, theweights of the combination being explicitly computable.Comment: 20 pages, one figur

The asymmetric simple exclusion model with multiple shocks