"Not to change the subject but..." Oh, there's no change of subject at all (relative to the discussion of Random Evolutions). It seems with your mentioning of geodesics that we are back talking about harmonic functions.
SteveG, did you happen to read the Scientific American paper that RogerF and I referenced? Reuben's article gives what you may find an interesting insight into your earlier question regarding how the phenomenon of waves manifests from agent based actions. Reuben was concerned with PDEs of the hyperbolic type (like the wave equation) and the work he did with Richard established solutions for these equations via stochastic means.
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