%0 Journal Article
%T The variance of the shock in the HAD process
%A Cristian F. Coletti
%A Pablo A. Ferrari
%A Leandro P. R. Pimentel
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0801.2526v1