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Article Dans Une Revue Physica A: Statistical Mechanics and its Applications Année : 2008

The δn statistic for the β-Hermite ensemble

Gérard Le Caër
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Camille Male
Renaud Delannay

Résumé

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.

Dates et versions

hal-00673374 , version 1 (23-02-2012)

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Citer

Gérard Le Caër, Camille Male, Renaud Delannay. The δn statistic for the β-Hermite ensemble. Physica A: Statistical Mechanics and its Applications, 2008, 387 (14), pp.3384-3398. ⟨10.1016/J.PHYSA.2008.02.017⟩. ⟨hal-00673374⟩
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