Canonical Equation K ₂₈ for Normalized Spectral Functions of Random Symmetric Matrices with Identically Distributed Independent Blocks. Block Matrix Density. SS-Laws

Abstract

The first asymptotics of normalized spectral functions of random matrices were obtained for the matrices with independent entries. As we have seen in the previous chapter, it is possible to find the general form of possible limit normalized spectral functions of random symmetric matrices with asymptotically independent random blocks. But this general view of n.s.f. expressed through the solution of the corresponding canonical equation has a complicated form. Therefore, it is interesting to analyze this canonical equation for a special case, for example, where all blocks of a random matrix are identically distributed. We show that, in this case, it is possible to find the limit density of n.s.f. (we call it Block Matrix Density)