The random walk on upper triangular matrices over $\mathbb{Z}/m \mathbb{Z}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866915129895944192 |
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| author | Nestoridi, Evita Sly, Allan |
| author_facet | Nestoridi, Evita Sly, Allan |
| contents | We study a natural random walk on the $n \times n$ upper triangular matrices, with entries in $\mathbb{Z}/m \mathbb{Z}$, generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is $O(m^2n \log n+ n^2 m^{o(1)})$. This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_08731 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The random walk on upper triangular matrices over $\mathbb{Z}/m \mathbb{Z}$ Nestoridi, Evita Sly, Allan Probability Combinatorics We study a natural random walk on the $n \times n$ upper triangular matrices, with entries in $\mathbb{Z}/m \mathbb{Z}$, generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this random walk is $O(m^2n \log n+ n^2 m^{o(1)})$. This answers a question of Stong and of Arias-Castro, Diaconis, and Stanley. |
| title | The random walk on upper triangular matrices over $\mathbb{Z}/m \mathbb{Z}$ |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2012.08731 |