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Edge universality of correlated Gaussians. (English) Zbl 1421.15009

Summary: 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.

MSC:

15B52 Random matrices (algebraic aspects)
82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
60B20 Random matrices (probabilistic aspects)
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