Research ArticleNo Access
Bounds on the norm of Wigner-type random matrices
https://doi.org/10.1142/S2010326319500096Cited by:5 (Source: Crossref)
Abstract
We consider a Wigner-type ensemble, i.e. large hermitian random matrices with centered independent entries and with a general matrix of variances . The norm of 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 that substantially improves the earlier bound given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields 169 (2017) 667–727]. 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.
AMSC: 60B20, 60J10
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