Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5130110 | Stochastic Processes and their Applications | 2017 | 41 Pages |
Abstract
We study the dependence on ε in the critical dimension k(n,p,ε) for which one can find random sections of the âpn-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 nââ, which agree with the sharp estimates for the extreme values p=1 and p=â. Toward this end, we provide tight bounds for the Gaussian concentration of the âp-norm.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Grigoris Paouris, Petros Valettas, Joel Zinn,