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Mixing time of the upper triangular matrix walk over $\mathbb{Z}/m \mathbb{Z}$

Friday, January 31, 2020 - 2:55pm
"Mixing time of the upper triangular matrix walk over $\mathbb{Z}/m \mathbb{Z}$"

In joint work with Allan Sly, we study a natural random walk on the 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 $O(n^2m^2)$. This generalizes a result of Peres and Sly and answers a question of Stong, Arias-Castro, Diaconis and Stanley. When $m$ is prime, we get a sharper upper bound for the mixing time by using the work of Diaconis and Hough.