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Logarithmic moments of characteristic polynomials of random matrices

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  • Brézin, Edouard
  • Hikami, Shinobu

Abstract

In a recent article we have discussed the connections between averages of powers of Riemann's ζ-function on the critical line, and averages of characteristic polynomials of random matrices. The result for random matrices was shown to be universal, i.e., independent of the specific probability distribution, and the results were derived for arbitrary moments. This allows one to extend the previous results to logarithmic moments, for which we derive the explicit universal expressions in random matrix theory. We then compare these results to various results and conjectures for ζ-functions, and the correspondence is again striking.

Suggested Citation

  • Brézin, Edouard & Hikami, Shinobu, 2000. "Logarithmic moments of characteristic polynomials of random matrices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 333-341.
    • Handle: RePEc:eee:phsmap:v:279:y:2000:i:1:p:333-341
    DOI: 10.1016/S0378-4371(99)00584-1
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    Cited by:

    1. H. Kösters, 2011. "Characteristic Polynomials of Sample Covariance Matrices," Journal of Theoretical Probability, Springer, vol. 24(2), pages 545-576, June.
    2. Su, Zhonggen, 2010. "On the second-order correlation of characteristic polynomials of Hermite [beta] ensembles," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1500-1507, October.

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