Random walk on unipotent matrix groups
Random walk on unipotent matrix groups
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DOI：
10.24033/asens.2466
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发表时间：
2015-12
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影响因子：
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通讯作者：
P. Diaconis;Bob Hough
中科院分区：
文献类型：
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作者：
P. Diaconis;Bob Hough
介绍了一种新的证明幂零群上随机游动中心极限定理的方法。该方法是说明在一个局部中心极限定理的海森堡群，削弱了必要条件的驱动措施。作为第二个例子，该方法被用来研究行走的$n\times n$单上三角组的条目取模$p$。该方法允许对单个坐标的行为给出尖锐的答案：对角线上的坐标需要$p ^2 $步的随机性，第二对角线上的坐标需要$p$步;第k对角线上的坐标需要$p^{\frac{2}{k}}$步。
We introduce a new method for proving central limit theorems for random walk on nilpotent groups. The method is illustrated in a local central limit theorem on the Heisenberg group, weakening the necessary conditions on the driving measure. As a second illustration, the method is used to study walks on the $n\times n$ uni-upper triangular group with entries taken modulo $p$. The method allows sharp answers to the behavior of individual coordinates: coordinates immediately above the diagonal require order $p^2$ steps for randomness, coordinates on the second diagonal require order $p$ steps; coordinates on the $k$th diagonal require order $p^{\frac{2}{k}}$ steps.