## 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)

### Keywords:

universality; random matrix; correlation
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### References:

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