随机矩阵理论全局域的一种简便方法
A Simple Approach to Global Regime of the Random Matrix Theory
摘要：
本文讨论了高阶随机矩阵归一化特征值计数测度矩的渐近计算方法。该方法是基于预解式的身份和某些公式有关的期望，某些矩阵函数和期望，包括其衍生物，或等价地，在扰动理论的一些简单的公式。在这种独特的方法的框架下，我们得到的函数方程的斯蒂尔切斯变换的限制归一化特征值计数措施和界的收敛速率的大多数已知的随机矩阵合奏。
英文摘要：
We discuss a method of the asymptotic computation of moments of the normalized eigenvalue counting measure of random matrices of large order. The method is based on the resolvent identity and on some formulas relating expectations of certain matrix functions and the expectations including their derivatives or, equivalently, on some simple formulas of the perturbation theory. In the framework of this unique approach we obtain functional equations for the Stieltjes transforms of the limiting normalized eigenvalue counting measure and the bounds for the rate of convergence for the majority known random matrix ensembles.
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