论文标题
$ \ mathbb {z}/m \ mathbb {z} $上的上三角矩阵上的随机步行
The random walk on upper triangular matrices over $\mathbb{Z}/m \mathbb{Z}$
论文作者
论文摘要
我们在$ n \ times n $上三角矩阵上学习自然随机步行，其中包含$ \ mathbb {z}/m \ mathbb {z} $中的条目，该步骤由添加或在上面的行中添加或减去均匀随机行的步骤生成。我们表明，此随机步行的混合时间为$ O（m^2n \ log n+ n^2 m^{o（1）}）$。这回答了Stong和Arias-Castro，Diaconis和Stanley的问题。
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.
