由与渐近自由随机矩阵系综共轭所诱导的涨落矩
Fluctuation moments induced by conjugation with asymptotically liberating random matrix ensembles
AI总结：
本文研究常数矩阵经渐近自由随机矩阵系综共轭后产生的涨落矩与高阶矩，并确定了与离散傅里叶变换矩阵相关系综诱导的涨落矩。
摘要：
G. Anderson 和 B. Farrel 证明，常数矩阵经渐近自由随机酉矩阵共轭后会产生渐近自由独立性。独立的 Haar 酉随机矩阵和独立的 Haar 正交随机矩阵即是渐近自由系综的例子。本文研究常数矩阵经与渐近自由系综共轭所诱导的涨落矩及高阶矩。特别地，我们确定了由一个与离散傅里叶变换矩阵相关的系综所诱导的涨落矩。
英文摘要：
G. Anderson and B. Farrel showed that conjugation of constant matrices by asymptotically liberating random unitary matrices give rise to asymptotic free independence. Independent Haar-unitary random matrices and independent Haar-orthogonal random matrices are examples of asymptotically liberating ensembles. In this paper, we investigate the fluctuation moments, and higher order moments, induced on constant matrices by conjugation with asymptotically liberating ensembles. In particular, we determine fluctuation moments induced by an ensembles related to the Discrete Fourier Transform matrix.
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