Spectral density of complex eigenvalues and associated mean eigenvector self-overlaps at the edge of elliptic Ginibre ensembles
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| Format: | Preprint |
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2024
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| _version_ | 1866909247886852096 |
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| author | Crumpton, Mark J. Würfel, Tim R. |
| author_facet | Crumpton, Mark J. Würfel, Tim R. |
| contents | We consider the density of complex eigenvalues, $ρ(z)$, and the associated mean eigenvector self-overlaps, $\mathcal{O}(z)$, at the spectral edge of $N \times N$ real and complex elliptic Ginibre matrices, as $N \to \infty$. Two different regimes of ellipticity are studied: strong non-Hermiticity, keeping the ellipticity parameter $τ$ fixed and weak non-Hermiticity with $τ\rightarrow 1 $ as $N \rightarrow \infty$. At strong non-Hermiticity, we find that both $ρ(z)$ and $\mathcal{O}(z)$ have the same leading order behaviour across the elliptic Ginibre ensembles, establishing the expected universality. In the limit of weak non-Hermiticity, we find different results for $ρ(z)$ and $\mathcal{O}(z)$ across the two ensembles. This paper is the final of three papers that we have presented addressing the mean self-overlap of eigenvectors in these ensembles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_02103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral density of complex eigenvalues and associated mean eigenvector self-overlaps at the edge of elliptic Ginibre ensembles Crumpton, Mark J. Würfel, Tim R. Mathematical Physics We consider the density of complex eigenvalues, $ρ(z)$, and the associated mean eigenvector self-overlaps, $\mathcal{O}(z)$, at the spectral edge of $N \times N$ real and complex elliptic Ginibre matrices, as $N \to \infty$. Two different regimes of ellipticity are studied: strong non-Hermiticity, keeping the ellipticity parameter $τ$ fixed and weak non-Hermiticity with $τ\rightarrow 1 $ as $N \rightarrow \infty$. At strong non-Hermiticity, we find that both $ρ(z)$ and $\mathcal{O}(z)$ have the same leading order behaviour across the elliptic Ginibre ensembles, establishing the expected universality. In the limit of weak non-Hermiticity, we find different results for $ρ(z)$ and $\mathcal{O}(z)$ across the two ensembles. This paper is the final of three papers that we have presented addressing the mean self-overlap of eigenvectors in these ensembles. |
| title | Spectral density of complex eigenvalues and associated mean eigenvector self-overlaps at the edge of elliptic Ginibre ensembles |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2405.02103 |