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Bounds on the Norm of Wigner-type Random Matrices

Date: Tuesday, January 23, 2018 16:00 - 18:00
Speaker: Peter Mühlbacher (IST Austria)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Laszlo Erdös
Lab building west seminar room

Abstract:

We consider a Wigner-type ensemble, i.e. large hermitian $N\times N$ random matrices $H=H^*$ with centered independent entries and with a general matrix of variances $S_xy=\mathbb E|H_xy|^2$. The norm of $H$ is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of $S$ that substantially improves the earlier bound $2\| S\|^1/2_\infty$. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation.

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