Real spectra of large real asymmetric random matrices
arXiv:2104.02584 · doi:10.1103/PhysRevE.105.L012104
Abstract
When a randomness is introduced at the level of real matrix elements, depending on its particular realization, a pair of eigenvalues can appear as real or form a complex conjugate pair. We show that in the limit of large matrix size the density of such real eigenvalues is proportional to the square root of the asymptotic density of complex eigenvalues continuated to the real line. This relation allows one to calculate the real densities up to a normalization constant, which is then applied to various examples, including heavy-tailed ensembles and adjacency matrices of sparse random regular graphs.
5 pages, 3 figures
References in corpus (8)
- Dysonian dynamics of the Ginibre ensemble
- Truncations of Random Orthogonal Matrices
- General Eigenvalue Correlations for the Real Ginibre Ensemble
- Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
- Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
- The Brown measure of the sum of a self-adjoint element and an imaginary multiple of a semicircular element
- On the number of real eigenvalues of a product of truncated orthogonal random matrices
- Pseudo-hermitian random matrix theory: a review