Georgia Institute of Technology College of Sciences

Random matrix products perhaps among some of the most extensively studied examples of random dynamical systems, and moreover are central to the study of one-dimensional disordered systems. We discuss recent results by the author (joint with S. Raman) obtaining estimates on heavy-tailed random matrix products which are robust under perturbations in an appropriate sense, and hence "uniform" on compact sets of measures in an appropriate topology. We also discuss recent localization results for the Anderson model with heavy tails which make use of these uniform bounds.