Concentration of 1-Lipschitz maps into an infinite dimensional $\ell^p$-ball with $\ell^q$-distance function

Details Concentration of 1-Lipschitz maps into an infinite dimensional $\ell^p$-ball with $\ell^q$-distance function Concentration of 1-Lipschitz maps into an infinite dimensional $\ell^p$-ball with $\ell^q$-distance function

2008-08-24

arxiv.org/abs/0808.3238v1

Mathematics

Metric Geometry

11pages

Scientific paper

In this paper, we study the L\'{e}vy-Milman concentration phenomenon of
1-Lipschitz maps into infinite dimensional metric spaces. Our main theorem
asserts that the concentration to an infinite dimensional $\ell^p$-ball with
the $\ell^q$-distance function for $1\leq pconcentration to the real line.

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