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).*