Author

Bo'az Klartag

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Preprint Oct 2026

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...

Bo'az Klartag, Shahar Moshe · 0 citations

Preprint Jul 2026

Digesting the proof of the sharp thin-shell inequality

We present a proof that determines the optimal value of the universal constant in the thin-shell theorem for log-concave distributions in high dimensions. We prove that for any log-concave random vector $X = (X_1,\ldots,X_n)$ in $\mathbb{R}^n$ with mean zero and identity covariance, $$ {\rm Var}( |X|^2 ) \leq 8 n. $$ T...

Yuansi Chen, Bo'az Klartag · 9 citations · ⚡3