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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Highly, um, path dependent on the bearing of the first few steps.
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If distance and bearing is truly random (all bearings equally likely regardless of prev bearing) this is weakly true. If bearing is dependent (plus minus 20 from current bearing) this is strongly true.
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In your random walk, how often is the walker rolling the dice for a direction change?
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