Timeline for What are some of results in low dimensional statistics that do not hold in high dimensions?
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| Sep 19, 2022 at 17:50 | comment | added | Henry | I think you may have overstated the limiting variance of $\|X\|$, which I suspect is $\frac12$ rather than $1$, though it does not really affect your argument. It means for example that over $99.5\%$ of the probability is concentrated in the band $\sqrt{d}\pm 2$ for $d>3$ and this is your "concentrated around a sphere". This is not true for $d=1,2,3$ as $\sqrt{d}$ is not the best estimate of the centre of the distribution for small $d$; even for those small $d$ you have a high(er) concentration in a band of the same width such as $2 \pm2$ | |
| May 29, 2017 at 14:42 | history | edited | Henry.L | CC BY-SA 3.0 |
added 52 characters in body
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| May 29, 2017 at 14:34 | history | answered | Henry.L | CC BY-SA 3.0 |