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Equidistribution and β-ensembles
Tom Carroll; Jordi Marzo; Xavier Massaneda; Joaquim Ortega-Cerdà
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 2, p. 377-387

We find the precise rate at which the empirical measure associated to a β-ensemble converges to its limiting measure. In our setting the β-ensemble is a random point process on a compact complex manifold distributed according to the β power of a determinant of sections in a positive line bundle. A particular case is the spherical ensemble of generalized random eigenvalues of pairs of matrices with independent identically distributed Gaussian entries.

On trouve le taux précis où la mesure empirique associée à un β-ensemble converge vers sa mesure limite. Le β-ensemble est un processus de points aléatoires sur une variété complexe compacte répartis selon la puissance β d’un déterminant de sections d’un fibré de ligne positif. Un cas particulier est l’ensemble sphérique de valeurs propres généralisés de paires de matrices aléatoires avec entrées gaussiennes identiquement distribuées et independantes.

Published online : 2018-06-18
@article{AFST_2018_6_27_2_377_0,
     author = {Tom Carroll and Jordi Marzo and Xavier Massaneda and Joaquim Ortega-Cerd\`a},
     title = {Equidistribution and $\beta $-ensembles},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 27},
     number = {2},
     year = {2018},
     pages = {377-387},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2018_6_27_2_377_0}
}
Carroll, Tom; Marzo, Jordi; Massaneda, Xavier; Ortega-Cerdà, Joaquim. Equidistribution and $\beta $-ensembles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 2, pp. 377-387. afst.centre-mersenne.org/item/AFST_2018_6_27_2_377_0/

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