  We consider the totally asymmetric simple exclusion process with initial
conditions and/or jump rates such that shocks are generated. If the initial
condition is deterministic, then the shock at time t will have a width of order
t^{1/3}. We determine the law of particle positions in the large time limit
around the shock in a few models. In particular, we cover the case where at
both sides of the shock the process of the particle positions is asymptotically
described by the Airy_1 process. The limiting distribution is a product of two
distribution functions, which is a consequence of the fact that at the shock
two characteristics merge and of the slow decorrelation along the
characteristics. We show that the result generalizes to generic last passage
percolation models.
