Moment bounds and concentration inequalities for slowly mixing dynamical systems

Sébastien Gouëzel (1) , Ian Melbourne (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Warwick Mathematics Institute

We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit theorem with nonstandard scaling $(n\log n)^{1/2}$.

Domaines: Systèmes dynamiques [math.DS]

Sébastien Gouëzel, Ian Melbourne. Moment bounds and concentration inequalities for slowly mixing dynamical systems. 2014. ⟨hal-00971289v1⟩