Averages of ratios of characteristic polynomials for the compact classical groups
Averages of ratios of characteristic polynomials for the compact classical groups
复制标题
紧经典群的特征多项式比的平均值
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
N. Snaith
中科院分区：
文献类型：
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作者：
J. Conrey;P. Forrester;N. Snaith
紧典型群的特征多项式的比的估计是用行列式来计算的，行列式的维数与矩阵的秩无关。这些公式被证明是等价于表达式相同的平均值在以前的研究中，这是出于应用解析数论。我们的方法使用随机矩阵理论的经典方法，特别是行列式和正交多项式，并且可以被认为比以前的研究中使用的Howe对的方法更基本。
Averages of ratios of characteristic polynomials for the compact classical groups are evaluated in terms of determinants whose dimensions are independent of the matrix rank. These formulas are shown to be equivalent to expressions for the same averages obtained in a previous study, which was motivated by applications to analytic number theory. Our approach uses classical methods of random matrix theory, in particular determinants and orthogonal polynomials, and can be considered more elementary than the method of Howe pairs used in the previous study.