Canonical moments and random spectral measures

Abstract

We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical ensemble and e is a fixed unit vector. This random measure is a weighted sampling among the eigenvalues of A. We also study the large deviations properties of this random measure when the dimension of the matrix grows. The rate function for these large deviations involves the reversed Kullback information.

32 pages. Revised version accepted for publication in Journal of Theoretical Probability

References in corpus (6)

• On asymptotics of eigenvectors of large sample covariance matrix
• New scaling of Itzykson-Zuber integrals
• Asymptotic behavior of the Poisson--Dirichlet distribution for large mutation rate
• Large deviations for functions of two random projection matrices
• Large deviations for random matrix ensembles in mesoscopic physics
• Large Deviations for Random Power Moment Problem

Cited by in corpus (9)

• Distributions on unbounded moment spaces and random moment sequences
• High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses
• Fast sampling from $\beta$-ensembles
• Sum rules and large deviations for spectral measures on the unit circle
• Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble
• Moderate deviations for spectral measures of random matrix ensembles
• Large Deviations for Random Matricial Moment Problems
• Sum rules via large deviations
• Nonstandard limit theorems and large deviations for the Jacobi beta ensemble