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If I am doing a random walk I can expect to be sqrt(n) steps away from the origin after taking n steps. Is there anything I can expect about the *direction* though? I would think net direction would not drift much after a while. Max heading deviation = arctan(1/sqrt(n)) ...🤔
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Or more poetically: compared to origin your direction gets more and more narrowly defined. Compared to yourself a few steps ago, you are just as aimless as ever.
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