Stability of the matrix Dyson equation and random matrices with correlations

Ajanki OH, Erdos L, Krueger T (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Probability Theory and Related Fields Springer Verlag (Germany)

Book Volume: 173

Pages Range: 293-373

Journal Issue: 1-2

DOI: 10.1007/s00440-018-0835-z

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.

Authors with CRIS profile

Torben Krüger

Involved external institutions

IST Austria AT Austria (AT)

How to cite

APA:

Ajanki, O.H., Erdos, L., & Krueger, T. (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

MLA:

Ajanki, Oskari H., Laszlo Erdos, and Torben Krueger. "Stability of the matrix Dyson equation and random matrices with correlations." Probability Theory and Related Fields 173.1-2 (2019): 293-373.

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