Statistical limit laws: stability, rigorous computation, and quenched existence.
In the first half of the talk I will outline results concerning stability
with respect to various perturbations of the variance in a central limit
theorem, and the rate function in a large deviation principle. These
perturbations include those arising from numerical methods and also
allow us to estimate SRB measures of Anosov maps of the torus. In the
second half of the talk I will outline an extension of the powerful
spectral approach to proving limit laws like large deviations
principles and CLTs to the case of randomly driven dynamics.
Our approach remains spectral and we prove so-called "quenched" results,
which hold for almost-every initialisation of the driving system.