Almost sure rate of mixing for randomly perturbed Lorenz maps

In this thesis, I examine the long-term statistical behaviour of particular random one-dimensional discrete-time dynamical systems. In particular, I study a random expanding Lorenz system and a random contracting Lorenz system, and I show that both display exponential quenched decay of correlations for Hölder observables.

I achieve this by using random Young towers, in particular results from [8] and [26]. Specifically, I show that for both random systems, a return partition can be constructed on a suitable base with exponentially decaying tails. I then show that the resulting random Young tower satisfies the usual axioms to give us quenched decay of correlations on the random Young Tower itself, which I then relate back to the original random system.