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Oct 26 at 12:56 comment added Will Sawin @NateRiver Yes, although independence is not so strictly necessary since the law of large numbers is robust to many forms of dependence between the random variables and we only need a very weak form of the law of large numbers.
Oct 26 at 12:04 comment added Nate River Just noting for myself - the key here is a composition of iid random circle rotations is independent of its earlier iterates, just due to the niceness of uniformly chosen rotations. Very cool.
Oct 26 at 12:03 vote accept Nate River
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Oct 26 at 11:20 history edited Will Sawin CC BY-SA 4.0
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Oct 26 at 11:13 history answered Will Sawin CC BY-SA 4.0