The variance of the shock in the HAD process

Details The variance of the shock in the HAD process The variance of the shock in the HAD process

2008-01-16

arxiv.org/abs/0801.2526v1

Mathematics

Probability

Scientific paper

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.

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