# zbMATH — the first resource for mathematics

Analysis of the limiting spectral distribution of large dimensional random matrices. (English) Zbl 0872.60013
Summary: Results on the analytic behavior of the limiting spectral distribution of matrices of sample covariance type, studied by V. A. Marchenko and L. A. Pastur [Math. USSR, Sb. 1, 457-483 (1967); translation from Mat. Sb., n. Ser. 72(114), 507-536 (1967; Zbl 0152.16101)] and Y. Q. Yin [J. Multivariate Anal. 20, 50-68 (1986; Zbl 0614.62060)], are derived. Through an equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and resembles $$\sqrt {|x-x_0 |}$$ for most cases of $$x_0$$ in the boundary of its support. A complete analysis of a way to determine its support, originally outlined by Marchenko and Pastur (loc. cit.), is also presented.

##### MSC:
 6e+100 Distribution theory
##### Citations:
Zbl 0162.22501; Zbl 0152.16101; Zbl 0614.62060
Full Text: