标题： 非厄米矩阵系综中的Schur函数展开和特征多项式的平均值 显示英文标题

标题： Schur function expansion in non-Hermitian ensembles and averages of characteristic polynomials

摘要： 我们研究非厄米随机矩阵系综中特征多项式的$k$点关联函数，重点关注实数、复数和四元数$N \times N$吉尼布雷系综。 我们的方法基于特征展开技术，该技术将关联函数表示为涉及施尔函数的分拆求和。 我们展示了如何通过交换$N$和$k$角色的表示形式重新求和这些展开式。 我们还提供了类似于施尔测度的特征展开的概率解释，将关联函数与某些杨图的顶行分布联系起来。 在更具体的例子中，我们根据$k \times k$行列式或普拉夫斯行列式显式计算这些表达式。 我们证明了我们的方法可以扩展到其他系综，例如随机酉矩阵的截断。 显示英文摘要

摘要： We study $k$-point correlators of characteristic polynomials in non-Hermitian ensembles of random matrices, focusing on the real, complex and quaternion $N \times N$ Ginibre ensembles. Our approach is based on the technique of character expansions, which expresses the correlator as a sum over partitions involving Schur functions. We show how to re-sum the expansions in terms of representations which interchange the roles of $N$ and $k$. We also provide a probabilistic interpretation of the character expansion analogous to the Schur measure, linking the correlators to the distribution of the top row in certain Young diagrams. In more specific examples we evaluate these expressions explicitly in terms of $k \times k$ determinants or Pfaffians. We show that our approach extends to other ensembles, such as truncations of random unitary matrices.