Timeline for Magnitude of the sum of complex i.u.d. random variables in the unit circle
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 25, 2012 at 23:45 | comment | added | cardinal | To be precise, so as not to mislead, the above-referenced link uses a different (but related) distribution for the $Z_i$. | |
| Feb 25, 2012 at 23:28 | comment | added | cardinal | Here is a similar (recent) question at math.SE, though they were interested in the asymptotics of the expected value $\mathbf E M_n$: math.stackexchange.com/questions/99389 | |
| Feb 25, 2012 at 13:43 | answer | added | Douglas Zare | timeline score: 2 | |
| Feb 25, 2012 at 13:12 | comment | added | Erik Aas | The central limit theorem (en.wikipedia.org/wiki/central_limit_theorem ) applied to the real and imaginary parts of \sum _k Z_k shows these are normally distributed and independent. From this it should be easy to show $M_n = O(\sqrt n )$ with high probability. | |
| Feb 25, 2012 at 11:41 | answer | added | Brendan McKay | timeline score: 2 | |
| Feb 25, 2012 at 11:23 | history | asked | Richard Bonne | CC BY-SA 3.0 |