Structure of random discrete spacetime

The usual picture of spacetime consists of a continuous manifold, together with a metric of Lorentzian signature which imposes a causal structure. We consider a model in which spacetime consists of a discrete set of points taken at random from a manifold, with only the causal structure remaining. Using only this structure, we show how to construct a metric, how to define the effective dimension, and how such quantities may depend on the scale of measurement. We discuss possible desirable features of the model.