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arXiv · 2012.08731

The random walk on upper triangular matrices over $\mathbb{Z}/m \mathbb{Z}$

Evita Nestoridi·Allan Sly
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Abstract

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.

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Evita Nestoridi, Allan Sly. 2020-12-16. The random walk on upper triangular matrices over $\mathbb{Z}/m \mathbb{Z}$. https://arxiv.org/abs/2012.08731

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