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https://twitter.com/shoyer/status/1353021554959872001In other words, for a random point in the ball, the marginal in any direction will converge to a Gaussian (one line calc!). Maybe this doesn't look like your usual CLT. But consider Bernoulli CLT: 1/sqrt(n) sum_i X_i = <X, u>, with X random in {-1,1}^n & u=1/sqrt(n)*(1,..,1).