Concentration of the distance in finite dimensional normed spaces

Citation
J. Arias-de-reyna et al., Concentration of the distance in finite dimensional normed spaces, MATHEMATIKA, 45(90), 1998, pp. 245-252
Citations number
19
Categorie Soggetti
Mathematics
Journal title
MATHEMATIKA
ISSN journal
00255793 → ACNP
Volume
45
Issue
90
Year of publication
1998
Part
2
Pages
245 - 252
Database
ISI
SICI code
0025-5793(199812)45:90<245:COTDIF>2.0.ZU;2-B
Abstract
We prove that in every finite dimensional normed space, for "most" pairs (x , y) of points in the unit ball, \\x-v\\ is more than root 2(1 - epsilon). As a consequence, we obtain a result proved by Bourgain, using QS-decomposi tion, that guarantees an exponentially large number of points in the unit b all any two of which are separated by more than root 2(1 - epsilon).