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–Bloch–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.

中文翻译：

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与希尔方程相关的随机奇异矩阵乘积具有显式方差的 CLT

我们证明了与 Adams-Bloch-Lagarias 研究的随机希尔方程相关的一类随机奇异矩阵的乘积的中心极限定理 (CLT)。CLT 在矩阵条目的分布方面具有显式的方差公式，这允许在某些示例中进行精确计算。我们的证明依赖于与米- 依赖序列，这也导致有趣且精确的非退化条件。