Eigenvalues distribution for products of independent spherical ensembles
We consider the product of independent spherical ensembles. By the special structure of eigenvalues as a rotation invariant determinant point process, we show that the empirical spectral distribution of the product converges, with probability one, to a non random distribution. And the limiting eigenvalue distribution is a power of spherical law. We also present an interesting correspondence between the eigenvalues of three classes of random matrix ensembles and zeros of random polynomials.