Saddle points in the chaotic analytic function and Ginibre characteristic polynomial
Saddle points in the chaotic analytic function and Ginibre characteristic polynomial
复制标题
混沌解析函数和Ginibre特征多项式中的鞍点
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Hannay
中科院分区：
文献类型：
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作者：
Mark R. Dennis;J. Hannay
比较了混沌解析函数和Ginibre系综特征多项式中鞍点的分布。将这些无限多项式的对数导数实现为库仑电荷在零点处分布的电场，一个简单的平均场静电论证表明，鞍点减去零点的密度福尔斯下降为π−1| z|-4从原点开始。这种行为是一般的有限或无限多项式的零均匀随机分布在复平面上，并排斥。
Comparison is made between the distribution of saddle points in the chaotic analytic function and in the characteristic polynomials of the Ginibre ensemble. Realizing the logarithmic derivative of these infinite polynomials as the electric field of a distribution of Coulombic charges at the zeros, a simple mean-field electrostatic argument shows that the density of saddles minus zeros falls off as π−1 |z|−4 from the origin. This behaviour is expected to be general for finite or infinite polynomials with zeros uniformly randomly distributed in the complex plane, and which repel.