The Subdominant Eigenvalue of Möbius Monotone Transition Probability Matrix
We establish a Perron–Frobenius-type theorem for the subdominant eigenvalue of Möbius monotone transition matrices defined on partially ordered state spaces. This result extends the classical work of Keilson and Kester, where they considered stochastically monotone transition matrices in a totally o...
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MDPI AG
2025-06-01
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| author | Pei-Sen Li Pan Zhao |
| author_facet | Pei-Sen Li Pan Zhao |
| author_sort | Pei-Sen Li |
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| description | We establish a Perron–Frobenius-type theorem for the subdominant eigenvalue of Möbius monotone transition matrices defined on partially ordered state spaces. This result extends the classical work of Keilson and Kester, where they considered stochastically monotone transition matrices in a totally ordered setting. Furthermore, we show that this subdominant eigenvalue is the geometric ergodicity rate. |
| format | Article |
| id | doaj-art-fa61b8eb516e44cbba1a5fae721dec70 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-fa61b8eb516e44cbba1a5fae721dec702025-08-20T03:58:30ZengMDPI AGAxioms2075-16802025-06-0114749310.3390/axioms14070493The Subdominant Eigenvalue of Möbius Monotone Transition Probability MatrixPei-Sen Li0Pan Zhao1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100872, ChinaInstitute of Mathematics and Physics, Beijing Union University, Beijing 100101, ChinaWe establish a Perron–Frobenius-type theorem for the subdominant eigenvalue of Möbius monotone transition matrices defined on partially ordered state spaces. This result extends the classical work of Keilson and Kester, where they considered stochastically monotone transition matrices in a totally ordered setting. Furthermore, we show that this subdominant eigenvalue is the geometric ergodicity rate.https://www.mdpi.com/2075-1680/14/7/493eigenvaluesMöbius monotonepartially ordered spacesPerron-Frobenius theorem |
| spellingShingle | Pei-Sen Li Pan Zhao The Subdominant Eigenvalue of Möbius Monotone Transition Probability Matrix Axioms eigenvalues Möbius monotone partially ordered spaces Perron-Frobenius theorem |
| title | The Subdominant Eigenvalue of Möbius Monotone Transition Probability Matrix |
| title_full | The Subdominant Eigenvalue of Möbius Monotone Transition Probability Matrix |
| title_fullStr | The Subdominant Eigenvalue of Möbius Monotone Transition Probability Matrix |
| title_full_unstemmed | The Subdominant Eigenvalue of Möbius Monotone Transition Probability Matrix |
| title_short | The Subdominant Eigenvalue of Möbius Monotone Transition Probability Matrix |
| title_sort | subdominant eigenvalue of mobius monotone transition probability matrix |
| topic | eigenvalues Möbius monotone partially ordered spaces Perron-Frobenius theorem |
| url | https://www.mdpi.com/2075-1680/14/7/493 |
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