Benthen Zeegers - Statistical properties of random intermittent systems

For nonuniformly hyperbolic dynamical systems where the evolution map is deterministic there exists a fair amount of literature on statistical properties like decay of correlations and limit laws such as CLT. Much less is known for nonuniformly hyperbolic dynamical systems where the evolution map is random. In this talk we consider a class of random interval maps that are composed of two types of maps: regular and chaotic maps. These random models exhibit dynamical features of both types of maps by alternating between periods of either chaotic behaviour or being in a seemingly steady state, a phenomenon that is referred to as intermittency. We discuss results on the existence of a finite absolutely continuous invariant measure for these random models as well as results on decay of correlations.