论文标题
随机$ p $ - 亚种矩阵的共同分布
Joint distribution of the cokernels of random $p$-adic matrices
论文作者
论文摘要
在本文中，我们研究了随机$ p $ - adic矩阵的共同分布。令$ p $为prime，$ p_1（t），\ cdots，p_l（t）\ in \ mathbb {z} _p [t] $是nocion polyenmials，其还原$ p $ in $ \ mathbb {f} _p [t] _p [t] $ nistical and Intressible和irreduccible。我们确定cokernels $ \ text {cok}（p_1（a）），\ cdots，\ text {cok}（p_l（a））$的联合分布的限制，用于随机$ n \ times n \ times n $ matrix $ a $ a $ a $ a $ a $ a $ a $ \ mathbb {z} _p $ afty ting a haar c $ n of haar unfty。通过应用随机矩阵模型的线性化，我们还提供了一个概括，从而概括了该结果。最后，我们提供了一个足够的条件，即cokernels $ \ text {cok}（a）$和$ \ text {cok}（a+b_n）$作为$ n \ rightarrow \ infty $独立，其中$ b_n $是$ n \ times n \ times n $ n $ a $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ and $ n $ and $ and $ n $ and $ n $ and $ n $ and $ and $ n $ and $ n $ and $ n $ and $ n $ and $ and $ n $ and $ and $矩阵超过$ \ mathbb {z} _p $。
In this paper, we study the joint distribution of the cokernels of random $p$-adic matrices. Let $p$ be a prime and $P_1(t), \cdots, P_l(t) \in \mathbb{Z}_p[t]$ be monic polynomials whose reductions modulo $p$ in $\mathbb{F}_p[t]$ are distinct and irreducible. We determine the limit of the joint distribution of the cokernels $\text{cok} (P_1(A)), \cdots, \text{cok}(P_l(A))$ for a random $n \times n$ matrix $A$ over $\mathbb{Z}_p$ with respect to Haar measure as $n \rightarrow \infty$. By applying the linearization of a random matrix model, we also provide a conjecture which generalizes this result. Finally, we provide a sufficient condition that the cokernels $\text{cok}(A)$ and $\text{cok}(A+B_n)$ become independent as $n \rightarrow \infty$, where $B_n$ is a fixed $n \times n$ matrix over $\mathbb{Z}_p$ for each $n$ and $A$ is a random $n \times n$ matrix over $\mathbb{Z}_p$.
