Timeline for On average length of sums of unit vectors in R^n
Current License: CC BY-SA 3.0
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| Feb 19, 2013 at 5:24 | comment | added | TOM | Thank you, that is most useful and interesting! But still, the initial set is arbitrary - not random - I want to have a given large set of unit vectors (much larger than all other parameters) and then I want to take a random m-tuple of vectors from that set. Let us for simplicity agree that the sum of all vectors in A is 0, so that the mean of the random sample is 0. Then second moment of the length of a random m-tuple is at most m (straightforward calculation) and so the mean is at most sqrt(m) (by Cauchy-Schwarz). Thus we know that most of the sums lie within a ball of radius const*sqrt(m). | |
| Feb 19, 2013 at 2:04 | history | answered | Igor Rivin | CC BY-SA 3.0 |