Refined evaluation of the level-spacing distribution of symplectic ensembles: Moments and implications
Refined evaluation of the level-spacing distribution of symplectic ensembles: Moments and implications
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2006
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Gebremariam and Einstein, Refined evaluation of the level-spacing distribution of symplectic ensembles: Moments and implications. Physical Review E, 73, 2006.
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Abstract
To obtain a more precise value for the variance ?2 of the joint probability distribution of a symplectic ensemble, we extend previous numerical evaluations of a power series. Our result ?2?0.1041 shows that the excellent approximation using the analytically simple Wigner surmise fractionally overestimates this value. This behavior is important in establishing the trend of a generalization of the surmise to describe the terrace-width distribution on vicinal surfaces. We also obtain precise estimates of the skewness and the kurtosis of the exact distribution, as well as the related moments.