Random version of Dvoretzky’s theorem in ℓpn

Grigoris Paouris, Petros Valettas and Joel Zinn

Stochastic Processes and their Applications, 2017, vol. 127, issue 10, 3187-3227

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.

Keywords: Dvoretzky’s theorem; Random almost Euclidean sections; ℓpn spaces; Superconcentration; Concentration of measure; Gaussian analytic inequalities; Logarithmic Sobolev inequality; Talagrand’s L1−L2 bound; Variance of the ℓp norm (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414917300303
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:10:p:3187-3227

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2017.02.007

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().