Structured perturbations of tridiagonal twisted Toeplitz matrices
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917429464006656 |
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| author | Giandinoto, Dario Shapiro, Boris |
| author_facet | Giandinoto, Dario Shapiro, Boris |
| contents | Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We study the limiting statistical distribution of the eigenvalues of matrices of the form $R_n(a) = T_n(a) + σ_n X_n$, where $T_n(a)$ is a sequence of non-Hermitian tridiagonal twisted Toeplitz matrices, $X_n$ is a sequence of tridiagonal random matrices whose entries have mean $0$ and finite variance, and $σ_n\to0$. The limiting distribution turns out to be a two-dimensional measure which is in general different from the push-forward of the Lebesgue measure by the symbol. We also explain how the results could extend to banded non-Hermitian twisted Toeplitz matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20617 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structured perturbations of tridiagonal twisted Toeplitz matrices Giandinoto, Dario Shapiro, Boris Probability Spectral Theory Primary 15B52 Secondary 15B05, 47B28, 47B35, 47B36 Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We study the limiting statistical distribution of the eigenvalues of matrices of the form $R_n(a) = T_n(a) + σ_n X_n$, where $T_n(a)$ is a sequence of non-Hermitian tridiagonal twisted Toeplitz matrices, $X_n$ is a sequence of tridiagonal random matrices whose entries have mean $0$ and finite variance, and $σ_n\to0$. The limiting distribution turns out to be a two-dimensional measure which is in general different from the push-forward of the Lebesgue measure by the symbol. We also explain how the results could extend to banded non-Hermitian twisted Toeplitz matrices. |
| title | Structured perturbations of tridiagonal twisted Toeplitz matrices |
| topic | Probability Spectral Theory Primary 15B52 Secondary 15B05, 47B28, 47B35, 47B36 |
| url | https://arxiv.org/abs/2604.20617 |