有限局部环上随机矩阵普适性的动态观点
A dynamic point of view on universality for random matrices over finite local rings
AI总结：
本文通过动态观点证明，在有限局部环上，只要元素分布不集中于子环或理想的平移，独立同分布随机矩阵的角余核过程仍满足遍历定理，从而推广了均匀情形下的Cohen-Lenstra测度普适性。
AI中文摘要：
我们考虑有限局部环上独立同分布矩阵的余核角过程。当元素的分布是均匀的时，该过程是一个马尔可夫链，因此可以应用马尔可夫链的遍历定理。这特别意味着，对于均匀分布的p-adic随机矩阵，角余核几乎必然地按照Cohen-Lenstra测度分布。本注记的目的是证明，只要元素的分布不集中于某个子环的平移或某个理想的平移，遍历定理的结论对独立同分布矩阵也成立。这将由作者先前论文中证明的界得出。
英文摘要：
We consider the cokernel corners process for an i.i.d. matrix with entries in a finite local ring. When the distribution of the entries is uniform, this process is a Markov chain, and hence the ergodic theorem for Markov chains can be applied. This implies, in particular, that for uniformly distributed p-adic random matrices, the cokernels of the corners are distributed according to the Cohen-Lenstra measure, almost surely. The purpose of this note is to show that the conclusion of the ergodic theorem also holds for i.i.d matrices, provided that the distribution of the entries is not concentrated on the translate of a subring, or the translate of an ideal. This will follow from the bounds proved in a previous paper of the author.
