Finite-N fluctuation formulas for random matrices
TH Baker, PJ Forrester
JOURNAL OF STATISTICAL PHYSICS | PLENUM PUBL CORP | Published : 1997
For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic ΣNj = 1 (xj - 〈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 1/2ΣNj = 1 (0j - π) and - ΣNj = 1 log 2 |sin 0j/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 → ∞.