论文标题
混合力矩和随机组的联合分布
Mixed moments and the joint distribution of random groups
论文作者
论文摘要
我们研究随机阿贝尔和非阿贝尔群体的联合分布。在阿贝尔案中，我们证明了多个焦点的联合分布的随机$ p $ - 亚种矩阵的联合分布。在非亚伯式的情况下，我们计算由随机关系的自由亲群体的商给出的随机组的联合分布。在这两种情况下，我们都将已知的结果推广到随机$ p $ - 亚种矩阵和随机组的焦点的分布。我们的证明是基于观察结果，即混合力矩决定了随机组的联合分布，这将木材的作品扩展到阿贝尔群体的木材和非亚伯群体的锯蛋白。
We study the joint distribution of random abelian and non-abelian groups. In the abelian case, we prove several universality results for the joint distribution of the multiple cokernels for random $p$-adic matrices. In the non-abelian case, we compute the joint distribution of random groups given by the quotients of the free profinite group by random relations. In both cases, we generalize the known results on the distribution of the cokernels of random $p$-adic matrices and random groups. Our proofs are based on the observation that mixed moments determine the joint distribution of random groups, which extends the works of Wood for abelian groups and Sawin for non-abelian groups.
