论文标题
具有与Hill方程相关的随机奇异矩阵产品的明确差异的CLT
CLT with explicit variance for products of random singular matrices related to Hill's equation
论文作者
论文摘要
我们证明了与Adams $ \ unicode {x2013} $ bloch $ \ unicode {x2013} $ lagarias相关的一类随机单数矩阵的产物的中心限制定理（CLT）。 CLT在矩阵条目的分布方面具有差异的明确公式，这允许在某些示例中进行精确计算。我们的证明依赖于与$ m $依赖性序列理论的新联系，这也导致了有趣且精确的非修复条件。
We prove a central limit theorem (CLT) for the product of a class of random singular matrices related to a random Hill's equation studied by Adams$\unicode{x2013}$Bloch$\unicode{x2013}$Lagarias. The CLT features an explicit formula for the variance in terms of the distribution of the matrix entries and this allows for exact calculation in some examples. Our proof relies on a novel connection to the theory of $m$-dependent sequences which also leads to an interesting and precise nondegeneracy condition.
