Random version of Dvoretzky’s theorem in ℓpn
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© 2017 Elsevier B.V. We study the dependence on ε in the critical dimension k(n,p,ε) for which one can find random sections of the ℓ pn -ball which are (1+ε)-spherical. We give lower (and upper) estimates for k(n,p,ε) for all eligible values p and ε 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 ℓ p -norm.
author list (cited authors)
Paouris, G., Valettas, P., & Zinn, J.