Timeline for Averages of vector inner products over the Haar measure

9 events

when toggle format	what		by	license	comment
Mar 30, 2016 at 15:19	vote	accept	Henry Yuen
Mar 30, 2016 at 14:37	comment	added	Henry Yuen		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, 2016 at 14:28	comment	added	Carlo Beenakker		for the first formula, see equation B5 of arxiv.org/abs/cond-mat/9612179 ; measure of concentration: for large $d$ the elements of $\psi$ are independent Gaussians (zero mean, variance $1/d$)
Mar 30, 2016 at 14:22	comment	added	Henry Yuen		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, 2016 at 12:29	history	edited	Carlo Beenakker	CC BY-SA 3.0	deleted 7 characters in body
Mar 30, 2016 at 11:45	history	edited	Carlo Beenakker	CC BY-SA 3.0	added 72 characters in body
Mar 30, 2016 at 8:37	history	edited	Carlo Beenakker	CC BY-SA 3.0	added 319 characters in body
Mar 30, 2016 at 8:29	history	edited	Carlo Beenakker	CC BY-SA 3.0	added 319 characters in body
Mar 30, 2016 at 8:24	history	answered	Carlo Beenakker	CC BY-SA 3.0