One can pick a point on the surface of a unit hypersphere of any dimension by first picking a point in that dimension whose coordinates are all sampled from the normal distribution, then scaling by the distance to the origin, i.e., projecting to the (hyper-)sphere.

One can approximately sample from a normal distribution by sampling a bunch of times from any distribution satisfying the central limit theorem, then computing the mean (or just sum) of the samples.

Together, these seem potentially useful, though not sure what.

Project the endpoint of a random walk to unit distance.

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