Can the Hubble expansion be explained in terms of spacetime events undergoing a random walk?
There is a deterministic relation between the content of the universe and the Hubble expansion, at least in most (all?) of the cosmological models based on general relativity.
However Loren's suggestion is similar to E. A. Milne's Kinematic Relativity cosmology. (Relativity, Gravitation and World-Structure 1935) in which he first describes what is now known as 'K Calculus'.
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