The δn statistic for the β-Hermite ensemble

G. Le Caër, C. Male and R. Delannay

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 14, 3384-3398

Abstract: The fluctuation δn of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of N×N random matrices (GOE, GUE, GSE). It is investigated here for the β-Hermite ensemble as a function of the reciprocal of the temperature β by Monte Carlo simulations. The ensemble-averaged fluctuation 〈δn2〉 and the autocorrelation function vary logarithmically with n for any β>0 (1≪n≪N). The simple logarithmic behavior of the higher-order moments of δn, reported in the literature for the GOE (β=1) and the GUE (β=2), holds for any β>0 and is accounted for by Gaussian distributions whose variances depend linearly on lnn.

Keywords: Random matrix theory; Nearest-neighbor spacing; Simple logarithmic behavior (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:14:p:3384-3398

DOI: 10.1016/j.physa.2008.02.017

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