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2019 Edge universality of correlated Gaussians
Arka Adhikari, Ziliang Che
Electron. J. Probab. 24: 1-25 (2019). DOI: 10.1214/19-EJP273

Abstract

We consider a Gaussian random matrix with correlated entries that have a power law decay of order $d>2$ and prove universality for the extreme eigenvalues. A local law is proved using the self-consistent equation combined with a decomposition of the matrix. This local law along with concentration of eigenvalues around the edge allows us to get a bound for extreme eigenvalues. Using a recent result of the Dyson-Brownian motion, we prove universality of extreme eigenvalues.

Citation

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Arka Adhikari. Ziliang Che. "Edge universality of correlated Gaussians." Electron. J. Probab. 24 1 - 25, 2019. https://doi.org/10.1214/19-EJP273

Information

Received: 27 March 2018; Accepted: 31 January 2019; Published: 2019
First available in Project Euclid: 25 April 2019

zbMATH: 1421.15009
MathSciNet: MR3949269
Digital Object Identifier: 10.1214/19-EJP273

Subjects:
Primary: 15B52, 82B44

JOURNAL ARTICLE
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Vol.24 • 2019
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