Finite N Fluctuation Formulas for Random Matrices

Abstract

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic ${\sum }_{j=1}^N(x_j-<x>)$ 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 $\frac{1}{2}{\sum }_{j=1}^N({\theta }_j-\pi )$ 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 $N\to \infty$.

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

References in corpus (1)

• Distribution Functions for Random Variables for Ensembles of positive Hermitian Matrices

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