Quick math question: if you constrain a random walk so that the system does not respond to impulses in all but a tiny pizza slice, the distance from origin should grow in the slice direction linearly in number of steps, right? n instead of sqrt(n)?
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I assumed: at every epoch, choose a random angle a uniformly at random from [0, 2pi). If a < some small angle d, then take a step of length 1 in the direction of a. Otherwise, choose another angle. Repeat for n steps. How does distance from origin scale with n as d -> 0.
