Random version of Dvoretzky's theorem in l(p)(n)
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2017 Elsevier B.V. We study the dependence on in the critical dimension k(n,p,) for which one can find random sections of the pn -ball which are (1+)-spherical. We give lower (and upper) estimates for k(n,p,) for all eligible values p and as n, which agree with the sharp estimates for the extreme values p=1 and p=. Toward this end, we provide tight bounds for the Gaussian concentration of the p -norm.