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One way to do this is to ask yourself dumb questions; another is to relearn your field. Random walks on groups have been extensively studied during the past 30 years, with many such walks exhibiting what is known as a "cutoff phenomenon". (Loosely speaking, the random walk stays a long way from equilibrium for some time before converging to stationarity extremely fast -- the most famous result of this kind showed that approximately 7 riffle shuffles are required to randomise a deck of 52 playing cards.) Michael Bate and Stephen Connor have recently started to explore the concept of random walks on rings, a topic about which relatively little is known, using a mixture of ideas from probability and algebra (in particular, representation theory).
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Publisher: Pearson; CUSTOM EDITION FOR THE COLLEGE OF SOUTHERN NEVADA, 10TH EDITION edition (2010)
ISBN: 0558226086
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But it turns out that there are large classes of candidate universes that already show remarkably suggestive features. For example, any universe that has a notion of time with a certain robustness property turns out in an appropriate limit to exhibit special relativity [ 1, sect. 9.13 ]. And even more significantly, any universe that exhibits a certain conservation of finite dimensionality—as well as generating a certain level of effective microscopic randomness—will lead on a large scale to spacetime that follows Einstein's equations for general relativity [ 1, sect. 9.15 ] , source: Finite Mathematics and its Applications
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