The variance of the shock in the HAD process

2008/01/16 by Coletti, Cristian F., Ferrari, Pablo A., Pimentel, Leandro P. R.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0801.2526

Abstract

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 √ t and, as a corollary, prove a central limit theorem.

Related

• Hammersley's harness process: invariant distributions and height fluctuations
• Order of the variance in the discrete Hammersley process with boundaries
• Radial Dunkl Processes : Existence and uniqueness, Hitting time, Beta Processes and Random Matrices
• GUE × GUE limit law at hard shocks in ASEP
• t^1/3 fluctuation around the shock of TASEP with random initial condition