Finite- N fluctuation formulas for random matrices

Details Finite- N fluctuation formulas for random matrices Finite- N fluctuation formulas for random matrices

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996jsp....88.1371b&link_type=abstract

Journal of Statistical Physics, Volume 88, Issue 5-6, pp. 1371-1386

Physics

9

Random Matrices, Central Limit Theorem, Fluctuation Formulas, Toeplitz Determinants, Selberg Integral

Scientific paper

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 as N → ∞. 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 |sin θ 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 → ∞.

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