Stability of the Matrix Dyson Equation and Random Matrices with Correlations
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 d...
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| creator | Ajanki, Oskari Erdos, Laszlo Krüger, Torben |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1604.08188 |
| format | Article |
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| source | Open Access Journals; arXiv.org |
| subjects | Correlation Decay rate Eigenvalues Mathematical analysis Mathematics - Mathematical Physics Mathematics - Probability Matrix methods Physics - Mathematical Physics Stability analysis |
| title | Stability of the Matrix Dyson Equation and Random Matrices with Correlations |
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