Minkowski空间是Poisson过程的局部Noldus极限
Minkowski space is locally the Noldus limit of a Poisson process causet
摘要：
$\mathbb{R}^{d}$上的泊松过程$P_λ$具有继承自$\mathbb{R}^{d}$上的通常Minkowski度量的因果结构，具有由$λ^{1/d}c_{d}$归一化的最长因果链的高度给出的归一化离散因果距离$D_λ(x,y)$。我们证明了$P_λ$限制到一个紧集$Q$的概率收敛的意义上的Noldus $Q$与Minkowksi度量。
英文摘要：
A poisson process $P_λ$ on $\mathbb{R}^{d}$ with causal structure inherited from the the usual Minkowski metric on $\mathbb{R}^{d}$ has a normalised discrete causal distance $D_λ(x,y)$ given by the height of the longest causal chain normalised by $λ^{1/d}c_{d}$. We prove that $P_λ$ restricted to a compact set $Q$ converges in probability in the sense of Noldus to $Q$ with the Minkowksi metric.
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