The Edge Universality of Correlated Matrices

Arka Adhikari; Ziliang Che

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arXiv · 1712.04889

The Edge Universality of Correlated Matrices

Arka Adhikari·Ziliang Che

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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 an bound for extreme eigenvalues. Using a recent result of the Dyson-Brownian motion, we prove universality of extreme eigenvalues.

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Arka Adhikari, Ziliang Che. 2017-12-13. The Edge Universality of Correlated Matrices. https://arxiv.org/abs/1712.04889

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