Minkowski space is locally the Noldus limit of a Poisson process causet

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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