Inhomogeneous Circular Law for Correlated Matrices

@article{Alt2020InhomogeneousCL,
  title={Inhomogeneous Circular Law for Correlated Matrices},
  author={Johannes Alt and Torben Kruger},
  journal={arXiv: Probability},
  year={2020}
}
Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices
For a fixed quadratic polynomial $\mathfrak{p}$ in $n$ non-commuting variables, and $n$ independent $N\times N$ complex Ginibre matrices $X_1^N,\dots, X_n^N$, we establish the convergence of the
Non-Hermitian Random Matrices with a Variance Profile (II): Properties and Examples
For each $n$, let $A_n=(\sigma_{ij})$ be an $n\times n$ deterministic matrix and let $X_n=(X_{ij})$ be an $n\times n$ random matrix with i.i.d. centered entries of unit variance. In the companion
Local elliptic law
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
Optimal delocalization for generalized Wigner matrices
of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Eight Number Two May 2022
A list of forthcoming papers can be found online at http://www.bernoullisociety.org/index. php/publications/bernoulli-journal/bernoulli-journal-papers CONTENTS 713 BELLEC, P.C. and ZHANG, C.-H.
Randomly coupled differential equations with elliptic correlations
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

References

SHOWING 1-10 OF 56 REFERENCES
Spectral radius of random matrices with independent entries
We consider random $n\times n$ matrices $X$ with independent and centered entries and a general variance profile. We show that the spectral radius of $X$ converges with very high probability to the
Random matrices: Universality of local spectral statistics of non-Hermitian matrices
TLDR
This paper shows that a real n×n matrix whose entries are jointly independent, exponentially decaying and whose moments match the real Gaussian ensemble to fourth order has 2nπ−−√+o(n√) real eigenvalues asymptotically almost surely.
Local inhomogeneous circular law
We consider large random matrices $X$ with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in
Local laws for non-Hermitian random matrices
The product of m ∈ N independent random square matrices whose elements are independent identically distributed random variables with zero mean and unit variance is considered. It is known that, as
The local semicircle law for a general class of random matrices
We consider a general class of $N\times N$ random matrices whose entries $h_{ij}$ are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local
The circular law
The circular law theorem states that the empirical spectral distribution of a n×n random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex plane as
Fluctuation around the circular law for random matrices with real entries
We extend our recent result [Cipolloni, Erdős, Schroder 2019] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices $X$ with independent, identically distributed
Local circular law for random matrices
The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version
Location of the spectrum of Kronecker random matrices
For a general class of large non-Hermitian random block matrices $\mathbf{X}$ we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained
...
1
2
3
4
5
...