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constants/20.md

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@@ -41,8 +41,8 @@ where the supremum is over isotropic log-concave $X$ in $\mathbb R^n$. Any bound
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| Bound | Reference | Comments |
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| ----- | --------- | -------- |
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| $\sigma_n \le O\!\left(\sqrt{\frac{n}{\log n}}\right)$ | [K2007a] | First nontrivial bound. |
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| $\sigma_n \le O\!\left(n^{2/5+o(1)}\right)$ | [K2007b] | Improvement via power-law CLT methods. |
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| $\sigma_n \le O\left(\sqrt{\frac{n}{\log n}}\right)$ | [K2007a] | First nontrivial bound. |
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| $\sigma_n \le O\left(n^{2/5+o(1)}\right)$ | [K2007b] | Improvement via power-law CLT methods. |
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| $\sigma_n \le O(n^{3/8})$ | [Fle2010] | Further improvement. |
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| $\sigma_n \le O(n^{1/3})$ | [GM2011] | “Thin-shell / large deviation interpolation” bound. |
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| $\sigma_n \le O(n^{1/4})$ | [LV2017] | Via Eldan’s stochastic localization. |

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