Timeline for Expected norm of sum of random orthogonal matrices
Current License: CC BY-SA 3.0
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| Nov 5, 2011 at 21:09 | history | edited | Suvrit | CC BY-SA 3.0 |
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| Nov 5, 2011 at 20:09 | answer | added | Mikael de la Salle | timeline score: 8 | |
| Nov 5, 2011 at 19:52 | comment | added | Suvrit | @Terry: Ideally, non asymptotic results would be the best. I am, however, still curious about the limited asymptotic regimes where only one of $n$ or $d$ is allowed to be large (feels like the case of large $n$ should be easier). The Frobenius norm definitely seems much friendlier. | |
| Nov 5, 2011 at 19:49 | comment | added | Terry Tao | Conversely, in the regime where d is fixed and n is large, the classical central limit theorem should give good results, since the sum is going to be asymptotically a gaussian matrix (possibly shifted by a multiple of the identity, in the second question). | |
| Nov 5, 2011 at 19:47 | comment | added | Terry Tao | Are you interested in an asymptotic regime (e.g. n fixed, d large; or d fixed, n large)? I doubt there will be an exact formula otherwise; the operator norm is not algebraic enough for an algebraic miracle (as opposed to, say, the Frobenius norm). In the regime where n is fixed and d is large, free probability tools should in principle answer your question (or at least predict the answer). | |
| Nov 5, 2011 at 19:23 | history | asked | Suvrit | CC BY-SA 3.0 |