On the condensed density of the generalized eigenvalues of pencils of Hankel Gaussian random matrices and applications

Abstract

Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which allows to get a closed form approximation of the condensed density of the generalized eigenvalues of the pencils. Implications of this result for solving several moments problems are discussed and some numerical examples are provided.

30 pages, 16 figures, better approximations provided

References in corpus (3)

• A new transform for solving the noisy complex exponentials approximation problem
• Computational aspects and applications of a new transform for solving the complex exponentials approximation problem
• A diffusion equation for the density of the ratio of two jointly distributed Gaussian variables and the numerical inversion of Laplace transform

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• The limit empirical spectral distribution of complex matrix polynomials
• On the condensed density of the zeros of the Cauchy transform of a complex atomic random measure with Gaussian moments