Correlated random matrices: Band rigidity and edge universality

Alt, Johannes; Erdös, László; Krüger, Torben H; Schröder, Dominik J

Correlated random matrices: Band rigidity and edge universality

Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.

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https://arxiv.org/abs/1804.07744 [Preprint]

DOI

10.1214/19-AOP1379

Journal Article | Published | English

Scopus indexed

Author

Alt, Johannes^ISTA; Erdös, László^ISTA ; Krüger, Torben H^ISTA ; Schröder, Dominik J^ISTA

Department

Erdoes Group

Grant

Random matrices, universality and disordered quantum systems

Abstract

We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.

Publishing Year

2020

Date Published

2020-03-01

Journal Title

Annals of Probability

Publisher

Institute of Mathematical Statistics

Volume

Issue

Page

963-1001

ISSN

0091-1798

IST-REx-ID

6184

Cite this

Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 2020;48(2):963-1001. doi:10.1214/19-AOP1379

Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379

Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379.

J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” Annals of Probability, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.

Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.

Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379.

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