Description
Anderson's model in 1 dimension has been studied since the 80's and the location is well understood. Here I propose a new formula for the construction of the eigenvectors which makes the link with the products of independent random matrices. In particular, I show that, with a adapted scaling, eigenvectors behave as the exponential of a Brownian process with a drift, the drift corresponding to the classical localization result. This result is known for the product of independent random matrices but at our knowledge had not been generalized to Anderson's model.
