  We consider the totally asymmetric simple exclusion process with initial
conditions generating a shock. The fluctuations of particle positions are
asymptotically governed by the randomness around the two characteristic lines
joining at the shock. Unlike in previous papers, we describe the correlation in
space-time \emph{without} employing the mapping to the last passage
percolation, which fails to exists already for the partially asymmetric model.
We then consider a special case, where the asymptotic distribution is a cut-off
of the distribution of the largest eigenvalue of a finite GUE matrix. Finally
we discuss the strength of the probabilistic and physically motivated approach
and compare it with the mathematical difficulties of a direct computation.
