Timeline for Asymptotics of a ratio on the unit sphere
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 6 at 0:59 | history | edited | Drew Brady | CC BY-SA 4.0 |
deleted 3 characters in body
|
| Aug 5 at 23:29 | comment | added | Drew Brady | Perhaps a way to restate what you are saying is that (say by dominated convergence), $$ R_n^\star = \mathbb{E} \Big[\frac{a_n g_n^2}{\sum_{m=1}^\infty a_m g_m^2}\Big],$$ where the expectation is taken over the sequence $\{g_m\}_{m \geq 1}$ of iid standard Normals. | |
| Aug 5 at 23:20 | comment | added | fedja | Yes. The expectation of that will be the limit of your expectation as $k\to\infty$. | |
| Aug 5 at 22:21 | comment | added | fedja | In the limit you consider, the coordinates become iid centered Gaussians. | |
| Aug 5 at 22:00 | history | asked | Drew Brady | CC BY-SA 4.0 |