论文标题
多项式合奏中的产品平均值和特征多项式的比率
Averages of products and ratios of characteristic polynomials in polynomial ensembles
论文作者
论文摘要
多项式集合是确定点过程中的概率措施的子类。示例包括独立随机矩阵的产物，在Lyapunov指数上应用，以及具有外部场的随机矩阵，可以用作温度温度的量子场理论的示意图。我们首先分析了一般多项式集合中具有相等数量的特征多项式比率的期望值。使用Schur多项式，我们表明多项式集合构成Giambelli兼容点过程，从而导致按照随机矩阵的经典集合等比率的决定性公式。在第二部分中，我们引入了可逆的多项式集合，例如通过带有外部字段的随机矩阵。特征多项式的任意比率的期望值用多个轮廓积分表示。这将在复杂的Ginibre集合中的特征向量统计的背景下，这是一位作者的先前发现。
Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external field, that may serve as schematic models of quantum field theories with temperature. We first analyse expectation values of ratios of an equal number of characteristic polynomials in general polynomial ensembles. Using Schur polynomials we show that polynomial ensembles constitute Giambelli compatible point processes, leading to a determinant formula for such ratios as in classical ensembles of random matrices. In the second part we introduce invertible polynomial ensembles given e.g. by random matrices with an external field. Expectation values of arbitrary ratios of characteristic polynomials are expressed in terms of multiple contour integrals. This generalises previous findings by one of the authors for a single ratio in the context of eigenvector statistics in the complex Ginibre ensemble.
