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

Abstract

A poisson process $P_{\lambda }$ on ${\mathbb{R}}^d$ with causal structure inherited from the the usual Minkowski metric on ${\mathbb{R}}^d$ has a normalised discrete causal distance $D_{\lambda }(x,y)$ given by the height of the longest causal chain normalised by ${\lambda }^{1/d}{c}_d$. We prove that $P_{\lambda }$ restricted to a compact set $Q$ converges in probability in the sense of Noldus to $Q$ with the Minkowksi metric.

References in corpus (4)

• On Recovering Continuum Topology from a Causal Set
• A Lorentzian Gromov-Hausdoff notion of distance
• The limit space of a Cauchy sequence of globally hyperbolic spacetimes
• Emergent Continuum Spacetime from a Random, Discrete, Partial Order