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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Are we in one dimension here? In 1D, if you are a distance L away from the origin, then you will probably stay on the same side of the origin for a time ~L^2. Also, if you start at the origin, then the probability of making it to L without first returning to the origin is ~1/L.
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That’s a useful reduction. I guess the 2d equivalent would be to compute expected dwell time in a tolerance range, +/- theta from current heading
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I knew it! Among the elementary functions, your absolute *favorite* is the tangent!
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