Timeline for Asymptotics for minimum of a sequence of random variables
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| 4 hours ago | history | became hot network question | |||
| 8 hours ago | answer | added | Iosif Pinelis | timeline score: 5 | |
| 10 hours ago | comment | added | mathworker21 | @AlekseiKulikov I think by "max" you mean "min" (and by "$x_{2^k}$" you mean "$X_{2^k}$"). | |
| 11 hours ago | comment | added | Aleksei Kulikov | I believe we can show that almost surely $\limsup \frac{nY_n}{\log \log (n)} \le 10$, by defining $Z_k = \max(X_{2^{k-1}+1}, \ldots,x_{2^{k}})$ (they are now independent), bounding $Y_n$ for $2^{k}+1\le n \le 2^{k+1}$ from above by $Z_k$ and repeating your argument. | |
| 12 hours ago | comment | added | mathworker21 | The expected value is $\frac{1}{n+1}$, so it can't be that $Y_n = \frac{\log n}{n}$ almost surely (even with probability at least $\frac{1.01}{\log n}$). | |
| 12 hours ago | history | asked | Wojowu | CC BY-SA 4.0 |