Timeline for Estimation of the expected Euclidean distance between two random points on a unit $n$-hemisphere
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 23, 2020 at 6:14 | comment | added | user64494 | See that paper. | |
| Nov 21, 2020 at 18:12 | comment | added | flinty | Based on Roman's closed form in the previous question: Limit[2^(n - 1)*Gamma[n/2]^2/(Sqrt[\[Pi]]*Gamma[n - 1/2]), n -> \[Infinity]] is Sqrt[2]. | |
| Nov 21, 2020 at 17:53 | vote | accept | Penelope Benenati | ||
| Nov 21, 2020 at 17:50 | comment | added | flinty | In the limit for large $n$ the mean distance and distribution converge to the same results as the $n$-sphere distances. In other words, in high dimensions a single coordinate doesn't make much difference to the distances. Also I suspect for both spherical and hemispherical cases, the mean converges to $\sqrt{2}$ for high $n$ but that's just a guess. | |
| Nov 21, 2020 at 17:45 | history | answered | flinty | CC BY-SA 4.0 |