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

2008/08/24 by Kei Funano, Funano, Kei
Mathematics · #53C21 #53C23 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C21 #msc:53C23

paper · pdf · doi:10.48550/arxiv.0808.3238

11pages

arxiv created 2008/08/24 · arxiv updated 2009/12/01

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 ℓ^p-ball with the ℓ^q-distance function for 1≤ p<q≤ +∞ is equivalent to the concentration to the real line.

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