Central limit theorems in linear dynamics

Frédéric Bayart (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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 $f:X\to\mathbb K$, the sequence $(f+\dots+f\circ T^{n-1})/\sqrt n$ converges in distribution to a Gaussian random variable.

Domaines: Analyse fonctionnelle [math.FA]; Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Frédéric Bayart. Central limit theorems in linear dynamics. 2013. ⟨hal-00809499⟩