Stability of the matrix Dyson equation and random matrices with correlations

O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields (2018).

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Journal Article | Epub ahead of print | English
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Abstract
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.
Publishing Year
Date Published
2018-02-17
Journal Title
Probability Theory and Related Fields
Acknowledgement
Open access funding provided by Institute of Science and Technology (IST Austria).
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Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 2018. doi:10.1007/s00440-018-0835-z
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2018). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. https://doi.org/10.1007/s00440-018-0835-z
Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, 2018. https://doi.org/10.1007/s00440-018-0835-z.
O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, 2018.
Ajanki OH, Erdös L, Krüger TH. 2018. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields.
Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, Springer, 2018, doi:10.1007/s00440-018-0835-z.
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