On the failure of concentration for the \ell_\infty-ball

Tim Austin

Let $(X,d)$ be a compact metric space and $\mu$ a Borel probability on $X$. For each $N\ge 1$ let $d_{\infty }^N$ be the ${\ell }_{\infty }$-product on $X^N$ of copies of $d$, and consider $…