AI 中文总结
本文通过简单替代推导证明，阿贝尔p-群上随机过程为可逆马尔可夫链，且该性质从$\mathbb{Z}_p$推广至任意pro-finite局部环上的Haar随机矩阵。
AI 中文摘要
作者近期的工作研究了某些取值于阿贝尔p-群的随机过程，这些过程自然地出现在对$\mathbb{Z}_p$上Haar随机矩阵的研究中。令人有些惊讶的是，这些过程是可逆马尔可夫链。在本文中，我们给出了这一事实的一个简单替代推导。新的推导还证明了这一现象并非$\mathbb{Z}_p$所特有，而是推广到任何pro-finite局部环上的Haar随机矩阵。
英文摘要
Recent work of the author investigates certain random processes, valued in abelian p-groups, that naturally arise in the study of Haar random matrices over $\mathbb{Z}_p$. It was found, somewhat surprisingly, that these processes are reversible Markov chains. In this short note, we give a simple alternative derivation of this fact. The new derivation also proves that this phenomenon is not specific to $\mathbb{Z}_p$, but generalizes to Haar random matrices over any profinite local ring.
Comments15 pages. Comments welcome!
