Central and L^p-concentration of 1-Lipschitz maps into ℝ-trees

2008/01/09 by Kei Funano, Funano, Kei
Computer Science · Mathematics · #53C21 #53C23 #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Probability (math.PR) #Topological and Geometric Data Analysis #advanced mathematical theories #math.MG #math.PR #msc:53C21 #msc:53C23

paper · pdf · doi:10.48550/arxiv.0801.1371

18pages

openalex publication_date 2008/01/09 · arxiv created 2008/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Lévy-Milman concentration phenomenon of 1-Lipschitz maps from mm-spaces to ℝ-trees. Our main theorems assert that the concentration to ℝ-trees is equivalent to the concentration to the real line.

Related

• Concentration of 1-Lipschitz maps into an infinite dimensional ℓ^p-ball with ℓ^q-distance function
• Exponential and Gaussian concentration of 1-Lipschitz maps
• Observable concentration of mm-spaces into spaces with doubling measures
• Hamming graphs and concentration properties in non-quasi-reflexive Banach spaces
• Asymptotic smoothness, concentration properties in Banach spaces and applications