Jacobi polynomial moments and products of random matrices

Abstract

Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class of measures and characterize them by their moments essentially given by specific Jacobi polynomials with varying parameters. Solving this moment problem requires a study of the Riemann surfaces associated to a class of algebraic equations. The connection to random matrix theory is then established using methods from free probability.

References in corpus (6)

• Spectrum of the Product of Independent Random Gaussian Matrices
• Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices
• Eigenvalue statistics for product complex Wishart matrices
• On the Asymptotic Spectrum of Products of Independent Random Matrices
• Spectral density of products of Wishart dilute random matrices. Part I: the dense case
• Asymptotics for characteristic polynomials of Wishart type products of complex Gaussian and truncated unitary random matrices