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Mar 10, 2020 at 21:44 comment added Mateusz Kwaśnicki Interestingly, while the estimate given above is sharp at least when $\epsilon = \tfrac{1}{n}$ (consider a uniform distribution over $\frac{i}{n - 1}$, $i = 0, 1, \ldots, n - 1$), my guess is that the optimal value of $c$ is in fact $2$. However, I fail to see a proof.
Mar 10, 2020 at 14:52 history edited Denis Serre CC BY-SA 4.0
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Mar 10, 2020 at 12:53 vote accept kaleidoscop
Mar 10, 2020 at 12:34 history answered Mateusz Kwaśnicki CC BY-SA 4.0