Since its introduction in 1958, the 1-dimensional Anderson model of electron diffusion in random media has been of significant interest to physicists and mathematicians. Of particular concern is whether the model exhibits "spectral localization". Numerous localization results for iid potentials are known. Moreover, in the case of bounded potentials it is known that an assumption that potential values are given by identical distributions can be removed. We will discuss how one can remove an assumption of boundedness as well, using the recent results on random non-stationary matrix products. 

     In the first talk, we will cover the necessary background as well as spectral and dynamical tools that will be used in the proof.