论文标题
随机全态函数与实际零和随机Zeta函数的扩展的收敛性
Convergence of random holomorphic functions with real zeros and extensions of the stochastic zeta function
论文作者
论文摘要
在本文中，我们提供了一个统一的框架，用于研究来自各种经典集合的随机矩阵的重新定性多项式的收敛，以及Riemann Zeta函数的功能收敛结果。为此，我们考虑了收敛点过程的更一般的观点（特殊情况是从随机矩阵集成团体中收敛的特征值点过程的顺序），我们确定了足够的条件，在实际条件下，真实线上随机点过程的融合在法律中，在法律中，依法构成了均匀的范围，其均匀的质量是在法律中融合了均匀的范围，其质量是在均匀的范围内，其质量是在均匀的范围内，其质量是质量的质量，这些过程是均匀的质量范围。 经过考虑的。我们的结果扩展了各种作者获得的重新定性特征多项式的收敛结果（在循环单一合奏的情况下，有限的随机分析函数称为体形ZETA函数）。我们还表明，对于与这些有限的随机全态函数相关的广泛的点过程（我们通常可以将这些点解释为某些随机操作员的频谱），它们的stieltjes变换几乎是实际的cauchy分布的所有点，让人联想到Aizenman和warzel（\ cite）的结果（\ cite a aw15}）s n of cote n of cote，
In this article, we provide a unified framework for studying the convergence of rescaled characteristic polynomials of random matrices from various classical ensembles as well as functional convergence results for the Riemann zeta function. To this end, we consider the more general viewpoint of converging point processes (a special case of which is the sequence of converging eigenvalue point processes from random matrix ensembles), and we identify sufficient conditions under which the convergence of random point processes on the real line implies the convergence in law, for the topology of uniform convergence on compact sets, of suitable random holomorphic functions whose zeros are given by the point processes which are considered. Our results extend convergence results for rescaled characteristic polynomials obtained by various authors (in the case of the circular unitary ensemble, the limiting random analytic function is called the stochasic zeta function). We also show that for a wide class of point processes associated with these limiting random holomorphic functions (we can often interpret these points as the spectrum of some random operator), their Stieltjes transform follows for almost all points of the real line the standard Cauchy distribution, reminiscent of the results by Aizenman and Warzel (\cite{AW15}) in the case of the sine kernel point process.
