Bounds on the norm of Wigner-type random matrices

L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).


Journal Article | Published | English
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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.
Publishing Year
Date Published
2018-09-26
Journal Title
Random matrices: Theory and applications
Article Number
1950009
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Cite this

Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096
Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. https://doi.org/10.1142/s2010326319500096
Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 2018. https://doi.org/10.1142/s2010326319500096.
L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications, 2018.
Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications.
Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific Publishing, 2018, doi:10.1142/s2010326319500096.

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