# Random matrices with slow correlation decay

L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).

2019_Forum_Erdoes.pdf 1.52 MB

Journal Article | Published | English

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Abstract
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.
Publishing Year
Date Published
2019-03-26
Journal Title
Forum of Mathematics, Sigma
Volume
7
Article Number
e8
eISSN
IST-REx-ID

### Cite this

Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2
Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2019.2
Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University Press, 2019. https://doi.org/10.1017/fms.2019.2.
L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019.
Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.
Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.
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2019-09-17
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arXiv 1705.10661