具有对称完美配对的p群上的随机游走
A random walk on p-groups with a symmetric perfect pairing
AI总结：
该研究分析具有对称完美配对的p群上的随机游走，证明随机对称p进矩阵相关过程为马尔可夫链，其生成算子可明确描述且关于Cohen-Lenstra型测度可逆。
AI中文摘要：
随机对称p进矩阵的核是配备对称配对的随机阿贝尔群。若不仅考虑该矩阵，还考虑其左上角子矩阵，则得到取值于配备此类配对的阿贝尔群同构类的过程。我们证明，当矩阵为Haar随机时，该过程是马尔可夫链，由可明确描述的算子生成。我们还将证明，该算子关于Cohen-Lenstra型测度是可逆的。
英文摘要：
The kernel of a random symmetric p-adic matrix is a random abelian group, equipped with a symmetric pairing. If we consider not only the matrix but also its top-left corners, we get a process valued in isomorphism classes of abelian groups, equipped with such a pairing. We show that when the matrix is Haar random, this process is a Markov chain, generated by an operator that we explicitly describe. We will also prove that this operator is reversible with respect to a Cohen-Lenstra type measure.
