Finite- N fluctuation formulas for random matrices

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

Publishing date

Sep 1996

URL

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

Journals

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

Science

Physics

Additional info 2

9

Additional info 3

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

Type

Scientific paper

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 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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