A Simple Approach to Global Regime of the Random Matrix Theory

Details A Simple Approach to Global Regime of the Random Matrix Theory A Simple Approach to Global Regime of the Random Matrix Theory

1999-04-29

arxiv.org/abs/math/9904166v1

Mathematics

Spectral Theory

Scientific paper

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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