Finite N Fluctuation Formulas for Random Matrices

Details Finite N Fluctuation Formulas for Random Matrices Finite N Fluctuation Formulas for Random Matrices

1997-01-19

arxiv.org/abs/cond-mat/9701133v1

Physics

Condensed Matter

Statistical Mechanics

LaTeX 2.09, 11 pages + 3 eps figs (needs epsf.sty)

Scientific paper

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic $\sum_{j=1}^N (x_j - )$ is computed exactly and shown to satisfy a central limit theorem as $N \to \infty$. For the circular random matrix ensemble the p.d.f.'s for the linear statistics ${1 \over 2} \sum_{j=1}^N (\theta_j - \pi)$ and $- \sum_{j=1}^N \log 2|\sin \theta_j/2|$ 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 as $N \to \infty$.

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