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Dec 11, 2015 at 7:55 comment added Anthony Quas So I did a rough calculation for a higher-dimensional Gaussian, and got the same scaling. I'd still be quite surprised if that's universal.
Dec 10, 2015 at 6:13 comment added Anthony Quas I kind of agree, but it seems unlikely that you could ever obtain an $f(\epsilon)$ that was not of the form $C\cdot\epsilon$. I'll think about higher dimensional Gaussians later...
Dec 9, 2015 at 18:28 comment added Penghui Yao Thanks. In your example, do you mean $\epsilon'=\sqrt{\epsilon}$? That is good for the purpose. Here being dimension-independent means that $\epsilon'=f(\epsilon)$, which only depends on $\epsilon$. @Anthony Quas
Dec 9, 2015 at 8:09 history answered Anthony Quas CC BY-SA 3.0