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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.07125 |
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| _version_ | 1866916477177692160 |
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| author | Feng, Shi Gerencsér, Balázs |
| author_facet | Feng, Shi Gerencsér, Balázs |
| contents | Considering a Markov chain defined on a cycle, near-quadratic improvement of mixing is shown when only a subtle perturbation is introduced to the structure and non-reversible transition probabilities are used. More precisely, a mixing time of $O(n^{\frac{k+2}{k+1}})$ can be achieved by adding $k$ random edges to the cycle, keeping $k$ fixed while $n\to\infty$. The construction builds upon a biased random walk along the cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixing on the cycle with constant size perturbation Feng, Shi Gerencsér, Balázs Probability 60J10, 37A25 Considering a Markov chain defined on a cycle, near-quadratic improvement of mixing is shown when only a subtle perturbation is introduced to the structure and non-reversible transition probabilities are used. More precisely, a mixing time of $O(n^{\frac{k+2}{k+1}})$ can be achieved by adding $k$ random edges to the cycle, keeping $k$ fixed while $n\to\infty$. The construction builds upon a biased random walk along the cycle. |
| title | Mixing on the cycle with constant size perturbation |
| topic | Probability 60J10, 37A25 |
| url | https://arxiv.org/abs/2411.07125 |