On fluctuations of eigenvalues of random permutation matrices
Ben Arous, Gérard ; Dang, Kim
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015), p. 620-647 / Harvested from Numdam
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Les statistiques linéaires d’observables régulières du spectre de matrices de permutations, choisies aléatoirement sous une distribution générale de Ewens, donnent lieu à un phénomène intéressant de non-universalité. Bien qu’elles aient une variance bornée, leurs fluctuations ne sont pas asymptotiquement Gaussiennes, mais infiniment divisibles. Si l’observable est moins régulière, la variance diverge et les fluctuations sont Gaussiennes. Le degré de régularité est mesuré en termes de la qualité de l’approximation trapézoidale de l’intégrale de l’observable.

Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian but infinitely divisible. The fluctuations are asymptotically Gaussian for less smooth linear statistics for which the variance diverges. The degree of smoothness is measured in terms of the quality of the trapezoidal approximations of the integral of the observable.

Publié le : 2015-01-01
DOI : https://doi.org/10.1214/13-AIHP569
Classification:  60F05,  15B52,  60B20,  60B15,  60C05,  60E07,  65D30 
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     author = {Ben Arous, G\'erard and Dang, Kim},
     title = {On fluctuations of eigenvalues of random permutation matrices},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {51},
     year = {2015},
     pages = {620-647},
     doi = {10.1214/13-AIHP569},
     mrnumber = {3335019},
     language = {en},
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Ben Arous, Gérard; Dang, Kim. On fluctuations of eigenvalues of random permutation matrices. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) pp. 620-647. doi : 10.1214/13-AIHP569. http://gdmltest.u-ga.fr/item/AIHPB_2015__51_2_620_0/

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