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Fluctuation formula for complex random matrices

P. J. Forrester
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Abstract

A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict that the distribution will again be a Gaussian, with a specific mean and variance. The variance splits naturally into a bulk and surface contibution, the latter resulting from the long range correlations at the boundary of the support of the eigenvalue density.

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P. J. Forrester. 1998-05-24. Fluctuation formula for complex random matrices. https://arxiv.org/abs/cond-mat/9805306

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