Difference system for Selberg correlation integrals
Difference system for Selberg correlation integrals
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DOI：
10.1088/1751-8113/43/17/175202
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发表时间：
2010-04
期刊：
影响因子：
--
通讯作者：
P. Forrester;Masahiko Ito
中科院分区：
文献类型：
--
作者：
P. Forrester;Masahiko Ito
Selberg 相关积分是 Selberg 密度乘积的平均值。我们感兴趣的是 m = 1、μ1 = μ 的情况，此时这对应于相应特征多项式的 µ 阶矩。我们给出了确定平均值的变量 μ 中的 (n + 1) × (n + 1) 矩阵线性差分系统的显式形式，并给出了相应 (n + 1) × (n + 1) 矩阵的高斯分解。对于正整数 μ，差分系统可用于有效计算由该平均值定义的幂级数。
The Selberg correlation integrals are averages of the products with respect to the Selberg density. Our interest is in the case m = 1, μ1 = μ, when this corresponds to the µth moment of the corresponding characteristic polynomial. We give the explicit form of an (n + 1) × (n + 1) matrix linear difference system in the variable μ which determines the average, and we give the Gauss decomposition of the corresponding (n + 1) × (n + 1) matrix. For μ a positive integer the difference system can be used to efficiently compute the power series defined by this average.