Abstract
For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ Nj =1 (x j − 〈x〉) is computed exactly and shown to satisfy a central limit theorem asN → ∞. For the circular random matrix ensemble the p.d.f.’s for the statistics ½Σ Nj =1 (θ j −π) and − Σ Nj =1 log 2 |sinθ j/2| are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem asN → ∞.
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Communicated by J. L. Lebowitz
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Baker, T.H., Forrester, P.J. Finite-N fluctuation formulas for random matrices. J Stat Phys 88, 1371–1386 (1997). https://doi.org/10.1007/BF02732439
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DOI: https://doi.org/10.1007/BF02732439