Central limit theorems in linear dynamics

Bayart, Frédéric

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 $\mu$ sur $X$ telle que, pour de nombreuses fonctions $f:X\to 𝕂$, la suite $(f+\cdots +f\circ T^{n-1})/\sqrt{n}$ 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 $\mu$ on $X$ such that, for many functions $f:X\to 𝕂$, the sequence $(f+\cdots +f\circ T^{n-1})/\sqrt{n}$ converges in distribution to a Gaussian random variable.

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