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Canonical Moments and Random Spectral Measures

Author

Listed:
  • F. Gamboa

    (Université de Toulouse, Université Paul Sabatier)

  • A. Rouault

    (Université Versailles-Saint-Quentin)

Abstract

We study some connections between the random moment problem and 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 increases. The rate function for these large deviations involves the reversed Kullback information.

Suggested Citation

  • F. Gamboa & A. Rouault, 2010. "Canonical Moments and Random Spectral Measures," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1015-1038, December.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:4:d:10.1007_s10959-009-0239-1
    DOI: 10.1007/s10959-009-0239-1
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    References listed on IDEAS

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    1. Gamboa, F. & Rouault, A. & Zani, M., 1999. "A functional large deviations principle for quadratic forms of Gaussian stationary processes," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 299-308, July.
    2. A. Dawson, Donald & Feng, Shui, 2001. "Large deviations for the Fleming-Viot process with neutral mutation and selection, II," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 131-162, March.
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