Wigner矩阵的无穷小自由性
Infinitesimal Freeness of Wigner Matrices
AI总结：
本文在实无穷小自由概率框架下，通过环形非交叉划分与有向图的组合关系，计算独立复Wigner矩阵的无穷小累积量，证明其渐近实无穷小自由性，并特别指出矩阵与其转置的渐近无穷小自由性。
AI中文摘要：
本文在Cébron与第二作者引入的实无穷小自由概率框架内，计算了独立复Wigner矩阵的实无穷小自由累积量。我们的方法依赖于建立环形非交叉划分与有向图族之间的组合关系。作为结果，我们证明了独立复Wigner矩阵是渐近实无穷小自由的。特别地，我们（在温和条件下）表明复Wigner矩阵与其转置是渐近无穷小自由的。
英文摘要：
In this paper, within the framework of real infinitesimal free probability introduced by Cébron and the second author, we compute the real infinitesimal free cumulants of independent complex Wigner matrices. Our approach relies on establishing a combinatorial relation between annular non-crossing partitions and families of directed graphs. As a consequence, we demonstrate that independent complex Wigner matrices are asymptotically real infinitesimally free. In particular, we show (under mild conditions) that a complex Wigner matrix is asymptotically infinitesimally free from its transpose.
