Timeline for On average length of sums of unit vectors in R^n
Current License: CC BY-SA 3.0
9 events
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| Feb 19, 2013 at 23:44 | comment | added | fedja | There is one thing I fail to understand: what prohibits all vectors to be (almost) the same? Then the expectation of the length is $m$, not $\sqrt m$. Of course, then the variance is $0$, so that part is OK in this trivial example. | |
| Feb 19, 2013 at 2:04 | answer | added | Igor Rivin | timeline score: 1 | |
| Feb 19, 2013 at 1:56 | comment | added | Igor Rivin | @Per: I am not sure I understand your question: the mean value of the length of the sum, is not the same as the length of the mean of the sum. | |
| Feb 19, 2013 at 1:38 | comment | added | Brendan McKay | TOM, your reply to Per adds to my confusion. You refer to a finite set of vectors (all 0 except for a single 1) then you say "any vector of length 1" (of which there are infinitely many). You put your vectors in $R^n$, not $Z^n$, remember. What is the complete definition of $A$? | |
| Feb 18, 2013 at 3:06 | comment | added | TOM | Per Alexandersson: there are n vectors with 1 as a coordinate and we have exponentially many, so I clearly mean any vector of legth 1. Joseph O'Rourke: it is - it is the about the average length of a random sum x_1+...+x_m, that is, it's euclidean length. Douglas Zare: I think I have really meant what I have written. Anyhow, how should I use the CLT in this case? I really need just a bound on the variance of the length of such a sum, nothing more. | |
| Feb 17, 2013 at 19:58 | comment | added | Douglas Zare | It sounds like once you figure out what question you want to ask, the answer will be the Central Limit Theorem (for vector-valued summands, or for each coordinate if you don't mind losing a factor). If you mean something deeper than that, please clarify. | |
| Feb 17, 2013 at 14:58 | comment | added | Joseph O'Rourke | Is not the question asking for statistics for the total travel of a random walk, each of whose steps is of length $1$? | |
| Feb 17, 2013 at 14:23 | comment | added | Per Alexandersson | This seems strange; your unit vectors, are these (1,0,...) and (0,1,0,0,...) and so on, or just vectors of length 1? If the latter, the expected mean should be the zero vector then, no? | |
| Feb 17, 2013 at 12:29 | history | asked | TOM | CC BY-SA 3.0 |