@article{5971,
abstract = {We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=𝔼∣∣Hxy∣∣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∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (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.},
author = {Erdös, László and Mühlbacher, Peter},
issn = {2010-3263},
journal = {Random matrices: Theory and applications},
publisher = {World Scientific Publishing},
title = {{Bounds on the norm of Wigner-type random matrices}},
doi = {10.1142/s2010326319500096},
year = {2018},
}