  We consider the Hammersley-Aldous-Diaconis (HAD) process with sinks and
sources such that there is a microscopic shock at every time $t$; denote $Z(t)$
its position. We show that the mean and variance of $Z(t)$ are linear functions
of $t$ and compute explicitely the respective constants in function of the left
and right densities. Furthermore, we describe the dependence of $Z(t)$ on the
initial configuration in the scale $\sqrt t$ and, as a corollary, prove a
central limit theorem.
