Central limit theorems in linear dynamics
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 1131-1158.

Étant donné un opérateur T agissant sur un espace de Banach X, nous étudions l’existence d’une mesure de probabilité μ sur X telle que, pour de nombreuses fonctions f:X𝕂, la suite (f++fT n-1 )/n converge en loi vers une variable aléatoire gaussienne.

Given a bounded operator T on a Banach space X, we study the existence of a probability measure μ on X such that, for many functions f:X𝕂, the sequence (f++fT n-1 )/n converges in distribution to a Gaussian random variable.

DOI : https://doi.org/10.1214/13-AIHP585
Mots clés : hypercyclic operators, linear dynamics, ergodic theory, dynamical systems, central limit theorem
@article{AIHPB_2015__51_3_1131_0,
     author = {Bayart, Fr\'ed\'eric},
     title = {Central limit theorems in linear dynamics},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1131--1158},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {3},
     year = {2015},
     doi = {10.1214/13-AIHP585},
     mrnumber = {3365976},
     language = {en},
     url = {http://www.numdam.org/articles/10.1214/13-AIHP585/}
}
Bayart, Frédéric. Central limit theorems in linear dynamics. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 1131-1158. doi : 10.1214/13-AIHP585. http://www.numdam.org/articles/10.1214/13-AIHP585/

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