# Local elliptic law

@article{Alt2022LocalEL, title={Local elliptic law}, author={Johannes Alt and Torben Kruger}, journal={Bernoulli}, year={2022} }

The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We show this convergence on all mesoscopic scales slightly above the typical eigenvalue spacing in the bulk spectrum with an optimal convergence rate. As a corollary we obtain complete delocalisation for the corresponding eigenvectors in any basis.

## 2 Citations

Real eigenvalues of elliptic random matrices

- Mathematics
- 2021

We consider the real eigenvalues of an (N ×N) real elliptic Ginibre matrix whose entries are correlated through a non-Hermiticity parameter τN ∈ [0, 1]. In the almost-Hermitian regime where 1 − τN =…

Randomly coupled differential equations with elliptic correlations

- Mathematics
- 2019

We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures among the…

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