Abstract (EN)

We give a new expression for the law of the eigenvalues of the discrete Anderson model on the finite interval [0,N], in terms of two random processes starting at both ends of the interval. Using this formula, we deduce that the tail of the eigenvectors behaves approximately like exp(σB|n−k|−γ|n−k|4) where Bs is the Brownian motion and k is uniformly chosen in [0,N] independently of Bs. A similar result has recently been shown by B. Rifkind and B. Virag in the critical case, that is, when the random potential is multiplied by a factor 1N√