Stability of the matrix Dyson equation and random matrices with correlations

O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.

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Journal Article | Published | English
Department
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
2019-02-01
Journal Title
Probability Theory and Related Fields
Acknowledgement
Open access funding provided by Institute of Science and Technology (IST Austria).
Volume
173
Issue
1-2
Page
293–373
ISSN
eISSN
IST-REx-ID
429

Cite this

Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373. doi:10.1007/s00440-018-0835-z
Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields, 173(1–2), 293–373. 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 173, no. 1–2 (2019): 293–373. 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, vol. 173, no. 1–2, pp. 293–373, 2019.
Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 173(1–2), 293–373.
Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.
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2018-12-17
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