Moment bounds and concentration inequalities for slowly mixing dynamical   systems
  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 $(n\log n)^{1/2}$. 
S\'ebastien Gou\"ezel (IRMAR), Ian Melbourne
math.DS