Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415112 | Journal of Functional Analysis | 2015 | 16 Pages |
Abstract
We consider an nÃn matrix of the form A=UTV, with U, V some independent Haar-distributed unitary matrices and T a deterministic matrix. We prove that for kâ¼n1/6 and b2:=1nTr(|T|2), as n tends to infinity, we haveETr(Ak(Ak)â)â²b2k and E[|Tr(Ak)|2]â²b2k. This gives a simple proof (with slightly weakened hypothesis) of the convergence of the support in the Single Ring Theorem, improves the available error bound for this convergence from nâα to eâcn1/6 and proves that the rate of this convergence is at most nâ1/6logâ¡n.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Florent Benaych-Georges,