AI 中文总结
本文针对可逆独立随机矩阵乘积的范数对数，证明了非格型局部中心极限定理与埃奇沃思展开，还为文献[MatBE]的中心极限定理最优速率提供了新证明，并给出收缩的若干充分条件。
AI 中文摘要
我们针对可逆独立随机矩阵乘积的范数对数，证明了非格型局部中心极限定理及埃奇沃思展开。我们的条件包含收缩假设、矩阵支撑集“足够大”的假设，以及其分布足够正则的假设。作为证明的副产品，我们还能为文献[MatBE]中证明的中心极限定理最优速率提供另一种证明，与[MatBE]类似，我们给出了若干收缩的充分条件。
英文摘要
We prove a non-lattice local central limit theorem and Edgeworth expansions for the logarithm of the norms of products of invertible independent random matrices. Our conditions include a contraction assumption, an assumption that supports of the matrices are ``large enough" and their distributions are sufficiently regular. As a byproduct of the proof we are also able to provide a different proof to the optimal rates in the CLT proved in \cite{MatBE}. Like in \cite{MatBE} we provide several sufficient conditions for contraction.
Comments19 pp
