Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble as the set of N×N real nonsymmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if |i-j|
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Non-Hermitian diluted banded random matrices: Scaling of eigenfunction and spectral properties.
Phys Rev E
October 2024
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico.
Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble as the set of N×N real nonsymmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if |i-j| View Article and Find Full Text PDF
Analytic approach for the number statistics of non-Hermitian random matrices.
Phys Rev E
June 2021
Physics Institute, Federal University of Rio Grande do Sul, 91501-970 Porto Alegre, Brazil.
We introduce a powerful analytic method to study the statistics of the number N_{A}(γ) of eigenvalues inside any smooth Jordan curve γ∈C for infinitely large non-Hermitian random matrices A. Our generic approach can be applied to different random matrix ensembles of a mean-field type, even when the analytic expression for the joint distribution of eigenvalues is not known. We illustrate the method on the adjacency matrices of weighted random graphs with asymmetric couplings, for which standard random-matrix tools are inapplicable, and obtain explicit results for the diluted real Ginibre ensemble.
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