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  • 0 posts edited
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  • 24 votes cast
Mar
30
accepted Averages of vector inner products over the Haar measure
Mar
30
comment Averages of vector inner products over the Haar measure
Do you have a more precise estimate of the error (as a function of $d$) when you try to treat the elements of $\psi$ as independent Gaussians?
Mar
30
comment Averages of vector inner products over the Haar measure
Great, thanks! Where did you get the first formula, though? Also, as a followup: would you know what kind of measure of concentration is satisfied by these inner products? That is, what is the probability that $\mathrm{Tr}( \psi \psi^* \, \, w x^* \,\, \psi \psi^* \,\, y z^*)$ deviates from the average by more than some amount $\epsilon$?
Mar
30
asked Averages of vector inner products over the Haar measure
Sep
8
awarded  Taxonomist
Jul
10
awarded  Nice Question
Feb
27
revised A generalization of the Powers-Stormer inequality
edited tags
Feb
27
asked A generalization of the Powers-Stormer inequality
Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
May
22
comment A measure of closure under sumset?
Thanks, quid, for your answer, and the links to Hamidoune's work.
May
22
accepted A measure of closure under sumset?
May
22
revised A measure of closure under sumset?
added 138 characters in body
May
21
asked A measure of closure under sumset?
Apr
22
awarded  Yearling
Oct
9
accepted Multivariate Hensel's Lemma, but with only one polynomial
Oct
8
comment Multivariate Hensel's Lemma, but with only one polynomial
I have a quick clarification question: When you say "Suppose $Q(X_1,\ldots,X_n)$ is in $I^t$", you mean suppose there is are $\beta_1,\ldots,\beta_n\in R$ such that $Q(\beta_1,\ldots,\beta_n)\in I^t$? And then every time you write $\frac{dQ}{dX_1}$, you mean it is evaluated at the $\beta_1,\ldots,\beta_n$? If that's the case, then I interpret the mod $I^{t+1}$ solution as $\beta_1 + a_1,\ldots,\beta_n+a_n$. Thanks!
Oct
3
revised Multivariate Hensel's Lemma, but with only one polynomial
edited title
Oct
3
revised Multivariate Hensel's Lemma, but with only one polynomial
deleted 4 characters in body
Oct
3
accepted What is the relationship between singular value decomposition and solving linear systems?