Meeting times of Markov chains via singular value decomposition
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929412534960128 |
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| author | van Belle, Thomas Klimovsky, Anton |
| author_facet | van Belle, Thomas Klimovsky, Anton |
| contents | We suggest a non-asymptotic matrix perturbation-theoretic approach to get sharp bounds on the expected meeting time of random walks on large (possibly random) graphs. We provide a formula for the expected meeting time in terms of the singular value decomposition of the diagonally killed generator of a pair of independent random walks, which we view as a perturbation of the generator. Employing a rank-one approximation of the diagonally killed generator as the proof of concept, we work out sharp bounds on the expected meeting time of simple random walks on sufficiently dense Erdős-Rényi random graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Meeting times of Markov chains via singular value decomposition van Belle, Thomas Klimovsky, Anton Probability 60J10, 60K35, 47A55, 05C81, 05C80, 60B20 We suggest a non-asymptotic matrix perturbation-theoretic approach to get sharp bounds on the expected meeting time of random walks on large (possibly random) graphs. We provide a formula for the expected meeting time in terms of the singular value decomposition of the diagonally killed generator of a pair of independent random walks, which we view as a perturbation of the generator. Employing a rank-one approximation of the diagonally killed generator as the proof of concept, we work out sharp bounds on the expected meeting time of simple random walks on sufficiently dense Erdős-Rényi random graphs. |
| title | Meeting times of Markov chains via singular value decomposition |
| topic | Probability 60J10, 60K35, 47A55, 05C81, 05C80, 60B20 |
| url | https://arxiv.org/abs/2406.04958 |