Nonnegativity of the second largest eigenvalue of $4 \times 4$ tridiagonal stochastic matrices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917472234373120 |
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| author | Vagenende, Brando Verbeken, Brecht Guerry, Marie-Anne |
| author_facet | Vagenende, Brando Verbeken, Brecht Guerry, Marie-Anne |
| contents | The spectral study of nonnegative and more specifically stochastic matrices is an important topic in matrix theory. In this paper, we prove a conjecture, formulated by Ran and Teng, which states that the second largest eigenvalue of an irreducible $4\times4$ tridiagonal stochastic matrix is nonnegative. We establish this conjecture and extend the result to arbitrary $4\times4$ tridiagonal stochastic matrices, including both irreducible and reducible cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07591 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonnegativity of the second largest eigenvalue of $4 \times 4$ tridiagonal stochastic matrices Vagenende, Brando Verbeken, Brecht Guerry, Marie-Anne Probability 15A18, 15B51 The spectral study of nonnegative and more specifically stochastic matrices is an important topic in matrix theory. In this paper, we prove a conjecture, formulated by Ran and Teng, which states that the second largest eigenvalue of an irreducible $4\times4$ tridiagonal stochastic matrix is nonnegative. We establish this conjecture and extend the result to arbitrary $4\times4$ tridiagonal stochastic matrices, including both irreducible and reducible cases. |
| title | Nonnegativity of the second largest eigenvalue of $4 \times 4$ tridiagonal stochastic matrices |
| topic | Probability 15A18, 15B51 |
| url | https://arxiv.org/abs/2605.07591 |