This is an announcement for the paper "Random version of Dvoretzky's theorem in $\ell_p^n$" by Grigoris Paouris, Petros Valettas and Joel Zinn.
Abstract: We study the dependence on $\varepsilon$ in the critical dimension $k(n, p, \varepsilon)$ that one can find random sections of the $\ell_p^n$-ball which are $(1+\varepsilon)$-spherical. For any fixed $n$ we give lower estimates for $k(n, p, \varepsilon)$ for all eligible values $p$ and $\varepsilon$, which agree with the sharp estimates for the extreme values $p = 1$ and $p = \infty$. In order to do so, we provide bounds for the gaussian concentration of the $\ell_p$-norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B06, 46B07, 46B09
Remarks: 45 pages
Submitted from: valettasp@missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.07284
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