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Concentration of the distance between points in the unit ball

Ball, KM; Villa, R; (1998) Concentration of the distance between points in the unit ball. Mathematika , 45 245 - 252. 10.1112/S0025579300014182. Green open access

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Abstract

We prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ║x − y║ is more than √2(1 − ε). As a consequence, we obtain a result proved by Bourgain, using QS-decomposition, that guarantees an exponentially large number of points in the unit ball any two of which are separated by more than √2(1 − ε).

Type: Article
Title: Concentration of the distance between points in the unit ball
Open access status: An open access version is available from UCL Discovery
DOI: 10.1112/S0025579300014182
Publisher version: http://dx.doi.org/10.1112/S0025579300014182
Language: English
Additional information: © 1998 Cambridge University Press
Keywords: pure, FUNCTIONAL ANALYSIS, Isometric theory of Banach spaces
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/82460
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