The expanding Lorenz map, which is obtained by taking a Poincaré section of the geometric Lorenz attractor and quotienting along stable leaves, has been studied in the literature. In particular, in Díaz-Ordaz (2006) she proved using Young towers that it has exponential decay of correlations.
In this talk, I will consider a random dynamical system defined by taking an expanding Lorenz map and perturbing it at each time step. I will prove that for this random system, we have quenched decay of correlations by using random Young towers. This involves showing that one can construct a return partition on a suitable base, where the return time function has good asymptotics, and that the random tower map satisfies the usual tower axioms. It is then a question of showing that the dynamics on the random tower can be pulled back down to the original random system.
This talk is based on my paper Quenched decay of correlations for one-dimensional random Lorenz maps (DOI:10.1007/s10883-021-09583-w).