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

Abstract

In this paper, we study the Lévy-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 $1\le p<q\le +\infty$ is equivalent to the concentration to the real line.

11pages

References in corpus (1)

• Macroscopic dimension of the ${\ell }^p$-ball with respect to the ${\ell }^q$-norm