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Results tagged with measure-concentration
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user 1131
6
votes
Accepted
Variance modulo 1
On the one hand, the proof is very cheap. Let $Z_j=e^{2\pi iX_j}$. $X=\sum_j X_j$, $Z=e^{2\pi i X}$. Note that $\operatorname{Var}_{\mathbb R/\mathbb Z}X\approx 1-|EZ|$ and similarly for $X_j$ and $Z_ …
- 61.9k
7
votes
Accepted
Maximal inequality for the average of i.i.d. random variables
I streamlined my proof a bit so it is postable now :-)
First, a disclaimer. I have no doubt that there is some slick theorem dating back to 1980's that immediately implies what you want and all one n …
- 61.9k
6
votes
Accepted
Concentration of sum of concentrated random variables
There is a bad news and a good news. The bad one is that if you have no information other than that the probability of the $\varepsilon$-deviation is at most $p$ for each variable, then you can hardly …
- 61.9k
7
votes
Accepted
Lower tail of random rank one sums?
Warning: This is not a proper answer, just a dump of the thoughts I have had about this problem so far. Also, I'm not an expert in random matrix theory, so some bounds I'll be using may cry for improv …
- 61.9k
1
vote
Upper bound on the maxima of ratio of expectation of quantities under Gaussian measure
I guess exercise 4.4.5 from the Estimates of Integrals chapter (Section "Positive integrals") of Stewart's "Calculus" (parallel universe edition) may be helpful.
Let $\mu$ be a probability measure on …
- 61.9k