There is also a new method which gets a hold of eigenvectors directly by an iterative diagonalization procedure rather than indirectly via expectations of products of resolvents.
It is in the recent article <a href="http://arxiv.org/abs/1406.2957">"Multi-Scale Jacobi Method for Anderson Localization"</a> by John Imbrie.

I should add that the hot topic in the area now is many-body localization with tons of physics articles posted on the cond-mat section of arXiv. The above article by Imbrie can serve as an introduction to his other one about MBL: <a href="https://link.springer.com/article/10.1007/s10955-016-1508-x">"On many-body localization for quantum spin chains"</a> in JSP 2016.