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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -46,7 +46,7 @@ where the supremum is over isotropic log-concave $X$ in $\mathbb R^n$. Any bound
4646| $\sigma_n \le O(n^{3/8})$ | [ Fle2010] | Further improvement. |
4747| $\sigma_n \le O(n^{1/3})$ | [ GM2011] | “Thin-shell / large deviation interpolation” bound. |
4848| $\sigma_n \le O(n^{1/4})$ | [ LV2017] | Via Eldan’s stochastic localization. |
49- | $\sigma_n \le \exp\! \ bigl((\log n)^{1/2+o(1)}\bigr)=n^{o(1)}$ | [ Che2021] | First subpolynomial bound (via near-constant KLS). |
49+ | $\sigma_n \le \exp\bigl((\log n)^{1/2+o(1)}\bigr)=n^{o(1)}$ | [ Che2021] | First subpolynomial bound (via near-constant KLS). |
5050| $\sigma_n \le O(\log^4 n)$ | [ KL2022] | Polylog bound. |
5151| $\sigma_n \le O(\log^{2.23\ldots} n)$ | [ JLV2022] | Improves the polylog exponent. |
5252| $\sigma_n \le O(\sqrt{\log n})$ | [ K2023] | Further improvement. |
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