Statistical properties for irregular observables in slowly mixing hyperbolic systems

We prove various statistical properties (i.e., decay of correlations, central limit theorems with convergence rates, maximal large deviations and almost sure invariance principles) for non-smooth observables in the form of indicators functions in polynomially mixing hyperbolic dynamical systems. Such results were not known (or even expected to hold) for slowly mixing hyperbolic systems, although they are important for applications to physics and other sciences.