Finite-N fluctuation formulas for random matrices |
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Authors: | T H Baker P J Forrester |
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Institution: | (1) Department of Mathematics, University of Melbourne, 3052 Parkville, Victoria, Australia |
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Abstract: | For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ j N =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 j N =1 (θ j ?π) and ? Σ j N =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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Keywords: | Random matrices central limit theorem fluctuation formulas Toeplitz determinants Selberg integral |
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