HAD过程中冲击的方差
The variance of the shock in the HAD process
摘要：
考虑具有汇和源的Hammersley-Aldous-Diaconis（HAD）过程，使得在每一时刻都有一个微观激波$t$，用$Z(t)$表示它的位置.我们证明了$Z(t)$的均值和方差是$t$的线性函数，并明确地计算了左、右密度函数中的相应常数。此外，我们描述了$Z(t)$的依赖于初始配置的规模$\sqrt t$，并作为推论，证明了一个中心极限定理。
英文摘要：
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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