Shahar Moshe

A polynomial bound in Dvoretzky's theorem

We present a simple proof of the $\varepsilon$-Dvoretzky conjecture, which asserts that the dependence on the approximation parameter $\varepsilon$ in Dvoretzky's theorem is polynomial in $1/\varepsilon$. In particular, if $n \geq (C/\varepsilon)^{\ell/2+1}$, then any $n$-dimensional convex body has, through any given...