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We consider the Hammersley-Aldous-Diaconis (HAD) process with sinks andsources 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 functionsof $t$ and compute explicitely the respective constants in function of the leftand right densities. Furthermore, we describe the dependence of $Z(t)$ on theinitial configuration in the scale $\sqrt t$ and, as a corollary, prove acentral limit theorem.

The variance of the shock in the HAD process