Convergence of joint moments for independent random patterned matrices

Estimates for moments of random matrices with Gaussian elements

We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. We derive a system of recurrent relations for the moments and the covariance terms and develop a triangular scheme to prove the recurrent estimates. The estimates we obtain are asymptotically exact in the sense that they give exa...

A Note on Convergence of Moments for Random Young Tableaux

In recent work of Baik, Deift and Rains convergence of moments was established for the limiting joint distribution of the lengths of the first k rows in random Young tableaux. The main difficulty was obtaining a good estimate for the “tail” of the distribution and this was accomplished through a highly nontrival Riemann-Hilbert analysis. Here we give a simpler derivation. A conjecture is stated...

Dominated Convergence for Fuzzy Random Variables

Logarithmic moments of characteristic polynomials of random matrices

In a recent article we have discussed the connections between averages of powers of Riemann’s ζ-function on the critical line, and averages of characteristic polynomials of random matrices. The result for random matrices was shown to be universal, i.e. independent of the specific probability distribution, and the results were derived for arbitrary moments. This allows one to extend the previous...

Products of independent non-Hermitian random matrices

We consider the product of a finite number of non-Hermitian random matrices with i.i.d. centered entries of growing size. We assume that the entries have a finite moment of order bigger than two. We show that the empirical spectral distribution of the properly normalized product converges, almost surely, to a non-random, rotationally invariant distribution with compact support in the complex pl...