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Random version of Dvoretzky’s theorem in ℓpn

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  • Paouris, Grigoris
  • Valettas, Petros
  • Zinn, Joel

Abstract

We study the dependence on ε in the critical dimension k(n,p,ε) for which one can find random sections of the ℓpn-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 ℓp-norm.

Suggested Citation

  • Paouris, Grigoris & Valettas, Petros & Zinn, Joel, 2017. "Random version of Dvoretzky’s theorem in ℓpn," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3187-3227.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:10:p:3187-3227
    DOI: 10.1016/j.spa.2017.02.007
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    References listed on IDEAS

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    1. Tanguy, Kevin, 2015. "Some superconcentration inequalities for extrema of stationary Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 239-246.
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