Central and $L^p$-concentration of 1-Lipschitz maps into $\mathbb{R}$-trees

Abstract

In this paper, we study the L\'{e}vy-Milman concentration phenomenon of 1-Lipschitz maps from mm-spaces to $\mathbb{R}$-trees. Our main theorems assert that the concentration to $\mathbb{R}$-trees is equivalent to the concentration to the real line.