The V-Relation between Hermitian and Non-Hermitian Operators and Strong Law for Normalized Spectral Functions of Non-Selfadjoint Random Matrices with Independent Row Vectors

V.L. Girko

1998, v.4, №4, 499-507

ABSTRACT

The strong law for normalized spectral matrices of non-symmetric random matrices was proved by the author many years ago. In this paper, a methodological approach is presented which allows to obtain rigorous and simple proof of the strong Circular law and to describe the region where the eigenvalues of large non-Hermitian random matrices are distributed.

Keywords: $V$-transform,modified $V$-transform,martingale-differences method