Random projections of ℓ_p-balls satisfy a large deviations principle whose rate function is finite only on L_q-zonoids and given by a maximum entropy gap, with almost sure convergence to a Euclidean ball.
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Strange shadows of $\ell_p$-balls
Random projections of ℓ_p-balls satisfy a large deviations principle whose rate function is finite only on L_q-zonoids and given by a maximum entropy gap, with almost sure convergence to a Euclidean ball.