The weak Bruhat order for random walks on Coxeter groups
The weak Bruhat order for random walks on Coxeter groups
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Coxeter 群上随机游走的弱 Bruhat 阶
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Graham White
中科院分区：
文献类型：
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作者：
Graham White
我们证明了，对于由Coxeter生成元和恒等式生成的Coxeter群上的简单随机游动，处于任何两个态的概率都遵守弱Bruhat序。也就是说，在任何步骤之后，最可能的元素是恒等式，概率沿着从恒等式开始的任何测地线递减，并且如果群是有限的，最不可能的元素是最长的元素。当不同的生成器有不同的概率时，结果仍然是正确的，只要身份至少和其他任何一个一样可能。
We show that for the simple random walk on a Coxeter group generated by the Coxeter generators and identity, the likelihoods of being at any pair of states respect the weak Bruhat order. That is, after any number of steps, the most likely element is the identity, probabilities decrease along any geodesic from the identity, and the least likely element is the longest element, if the group is finite. The result remains true when different generators have different probabilities, so long as the identity is at least as likely as any other.