Concentration of 1-Lipschitz maps into an infinite dimensional ℓp-Ball with the ℓq-Distance function

Kei Funano

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

Concentration of 1-Lipschitz maps into an infinite dimensional ℓ^p-Ball with the ℓ^q-Distance function

Kei Funano

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we study the Levy-Milman concentration phenomenon of 1-Lipschitz maps into infinite dimensional metric spaces. Our main theorem asserts that the concentration to an infinite dimensional ℓ^p-ball with the ℓ^q-distance function for 1 ≤ p≤ q ≤ +∞ is equivalent to the concentration to the real line.

Original language	English
Pages (from-to)	2407-2417
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-09-09873-6
Publication status	Published - 2009 Jul 1

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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abstract = "In this paper, we study the Levy-Milman concentration phenomenon of 1-Lipschitz maps into infinite dimensional metric spaces. Our main theorem asserts that the concentration to an infinite dimensional ℓp-ball with the ℓq-distance function for 1 ≤ p≤ q ≤ +∞ is equivalent to the concentration to the real line.",

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