Canonical moments and random spectral measures

Details Canonical moments and random spectral measures Canonical moments and random spectral measures

2008-01-29

arxiv.org/abs/0801.4400v3

Mathematics

Probability

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

Scientific paper

10.1007/s10959-009-0239-1

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.

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