论文标题
复杂的Wigner矩阵的三阶矩
Third order moments of complex Wigner matrices
论文作者
论文摘要
我们计算复杂的Wigner矩阵的三阶矩。在商图方面，我们为三阶矩$α_{m_1，m_2，m_3} $提供了一个公式，$ t_ {m_1，m_1，m_3}^π$，其中$π$是kreweras在annulus上的非跨配对的kreweras。我们证明可以使用一组分区排列来计数这些图，这使我们可以用具有简单表达式的高阶空累积物来编写三阶矩。
We compute the third order moments of a complex Wigner matrix. We provide a formula for the third order moments $α_{m_1,m_2,m_3}$ in terms of quotient graphs $T_{m_1,m_2,m_3}^π$ where $π$ is the Kreweras complement of a non-crossing pairing on the annulus. We prove that these graphs can be counted using the set of partitioned permutations, this permits us to write the third order moments in terms of the high order free cumulants which have a simple expression.
