10.1142/s2010326319500096
Erdös, László
László
Erdös0000-0001-5366-9603
Mühlbacher, Peter
Peter
Mühlbacher
Bounds on the norm of Wigner-type random matrices
World Scientific Publishing
2018
2019-02-13T10:40:54Z
2020-01-21T12:01:12Z
journal_article
https://research-explorer.app.ist.ac.at/record/5971
https://research-explorer.app.ist.ac.at/record/5971.json
2010-3263
1802.05175
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.