Infinite mixing for one-dimensional maps with an indifferent fixed point

We study the properties of infinite-volume mixing for two classes of intermittent maps: expanding maps [0, 1] → [0, 1] with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding maps R^+ → R^+ with an indifferent fixed point at + ∞ preserving the Lebesgue measure. All maps have full branches. While certain properties are easily adjudicated, the so-called global-local mixing, namely the decorrelation of a global and a local observable, is harder to prove. We do this for two subclasses of systems. The first subclass includes, among others, the Farey map. The second class includes the standard Pomeau-Manneville map x → x + x^2 mod 1. Morevoer, we use global-local mixing to prove certain limit theorems for our intermittent maps.