Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896574 | Journal of Functional Analysis | 2018 | 28 Pages |
Abstract
We prove that for any 2
εEâZâ)â¤Cexpâ¡(âcminâ¡{αpε2n,(εn)2/p}),0<ε<1, where Z is the standard n-dimensional Gaussian vector, αp>0 is a constant depending only on p and C,c>0 are absolute constants. As a consequence we show optimal lower bound on the dimension of random almost spherical sections for these spaces. In particular, for any 2
0 is a constant depending only on p. This improves upon the previously known estimate due to Figiel, Lindenstrauss and Milman.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Grigoris Paouris, Petros Valettas,