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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -41,8 +41,8 @@ where the supremum is over isotropic log-concave $X$ in $\mathbb R^n$. Any bound
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4242| Bound | Reference | Comments |
4343| ----- | --------- | -------- |
44- | $\sigma_n \le O\! \ left(\sqrt{\frac{n}{\log n}}\right)$ | [ K2007a] | First nontrivial bound. |
45- | $\sigma_n \le O\! \ left(n^{2/5+o(1)}\right)$ | [ K2007b] | Improvement via power-law CLT methods. |
44+ | $\sigma_n \le O\left(\sqrt{\frac{n}{\log n}}\right)$ | [ K2007a] | First nontrivial bound. |
45+ | $\sigma_n \le O\left(n^{2/5+o(1)}\right)$ | [ K2007b] | Improvement via power-law CLT methods. |
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. |
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