Timeline for Probability of gaps between coordinates of a random point on the sphere
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2021 at 18:49 | answer | added | Iosif Pinelis | timeline score: 6 | |
| Feb 17, 2021 at 16:53 | comment | added | Hadi | Thanks for the answer. Actually what I am looking for is a formula for $\mathrm{Prob}(d,a)$ that can be used for estimates as $d\to\infty$ and $a\to 0$. In fact I am interested in an integral over the variable $a$. | |
| Feb 17, 2021 at 13:49 | comment | added | Alapan Das | The probability is probably $\frac{1}{R}\int_{0}^{R} P(x)dx$ where $P(x)=\frac{1}{S_{n-1}(s)}\max\{T(a,s), 0\}$. Here, $T(a,s)=S_{n-1}(s)-2(n-1)\frac{2\pi^{(n-2)/2}}{\Gamma((n-2)/2)}\int_{b}^{s} (s^2-y^2)^{(n-2)/2} dy$ Here, $s=\sqrt{R^2-{x_1}^2} ,b=\sqrt{{x_1}^2-a}$ and $S_{n}$ is surface area of $n$-sphere. | |
| Feb 17, 2021 at 7:39 | history | edited | gmvh |
Added top-level tag
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| Feb 17, 2021 at 3:49 | history | asked | Hadi | CC BY-SA 4.0 |