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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.08185 |
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| _version_ | 1866909807609380864 |
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| author | Ben-Hamou, Anna |
| author_facet | Ben-Hamou, Anna |
| contents | We consider a Markov chain on invertible $n\times n$ matrices with entries in $\mathbb{Z}_2$ which moves by picking an ordered pair of distinct rows and add the first one to the other, modulo $2$. We establish a logarithmic Sobolev inequality with constant $n^2$, which yields an upper bound of $O(n^2\log n)$ on the mixing time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08185 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixing time of a matrix random walk generated by elementary transvections Ben-Hamou, Anna Probability 60J10 We consider a Markov chain on invertible $n\times n$ matrices with entries in $\mathbb{Z}_2$ which moves by picking an ordered pair of distinct rows and add the first one to the other, modulo $2$. We establish a logarithmic Sobolev inequality with constant $n^2$, which yields an upper bound of $O(n^2\log n)$ on the mixing time. |
| title | Mixing time of a matrix random walk generated by elementary transvections |
| topic | Probability 60J10 |
| url | https://arxiv.org/abs/2503.08185 |