Timeline for Does projection of 3D points reduce distances by exactly 1/3?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 11, 2017 at 18:43 | history | edited | Will Sawin | CC BY-SA 3.0 |
edited body
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| Apr 10, 2017 at 21:34 | vote | accept | Joseph O'Rourke | ||
| Apr 10, 2017 at 0:24 | history | edited | dgulotta | CC BY-SA 3.0 |
clarify that I'm taking the large $n$ limit
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| Apr 10, 2017 at 0:12 | comment | added | dgulotta | The OP did not say in what sense $d=1/3$, so I assumed that the question was about whether the probability distribution for $d$ converges to the Dirac delta distribution at $1/3$ as $n \to \infty$. I will edit my answer to clarify. | |
| Apr 9, 2017 at 19:33 | comment | added | dgulotta | @ChristianRemling For large $n$, I would expect that $d(A,B)$ is usually very close to its expectation value. Since $(a_{ij}-b_{ij})^2$ and $(a_{kl}-b_{kl})^2$ are independent if $i,j,k,l$ are all different, the variance of $d(A,B)^2$ is $O(n^{-1})$. | |
| Apr 9, 2017 at 19:12 | comment | added | Joseph O'Rourke | And note: $\sqrt{2-\frac{3 \pi }{5}} \approx 0.339$. | |
| Apr 9, 2017 at 19:09 | history | answered | dgulotta | CC BY-SA 3.0 |