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Equidistribution and β-ensembles
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 2, pp. 377-387.

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.

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.

Publié le :
DOI : 10.5802/afst.1572
Tom Carroll 1 ; Jordi Marzo 2 ; Xavier Massaneda 2 ; Joaquim Ortega-Cerdà 2

1 University College Cork
2 Universitat de Barcelona, BGSMath
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     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},
     pages = {377--387},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 27},
     number = {2},
     year = {2018},
     doi = {10.5802/afst.1572},
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     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1572/}
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Tom Carroll; Jordi Marzo; Xavier Massaneda; Joaquim Ortega-Cerdà. Equidistribution and $\beta $-ensembles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 2, pp. 377-387. doi : 10.5802/afst.1572. https://afst.centre-mersenne.org/articles/10.5802/afst.1572/

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