Concentration of 1-Lipschitz maps into an infinite dimensional ℓ^{𝑝}-ball with the ℓ^{𝑞}-distance function

Funano, Kei

doi:10.1090/S0002-9939-09-09873-6

Concentration of $1$-Lipschitz maps into an infinite dimensional $\ell ^p$-ball with the $\ell ^q$-distance function
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Proc. Amer. Math. Soc. 137 (2009), 2407-2417 Request permission

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 $1\leq p<q\leq +\infty$ is equivalent to the concentration to the real line.

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