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

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
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9939-09-09873-6

Cite this

@article{8400a7afe8fa468dab3f2bf8ec0cf684,

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

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.",

author = "Kei Funano",

year = "2009",

month = jul,

doi = "10.1090/S0002-9939-09-09873-6",

language = "English",

volume = "137",

pages = "2407--2417",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "7",

}

TY - JOUR

T1 - Concentration of 1-Lipschitz maps into an infinite dimensional ℓp-Ball with the ℓq-Distance function

AU - Funano, Kei

PY - 2009/7

Y1 - 2009/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77951033294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951033294&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-09-09873-6

DO - 10.1090/S0002-9939-09-09873-6

M3 - Article

AN - SCOPUS:77951033294

VL - 137

SP - 2407

EP - 2417

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this