B. Derrida et Gj. Rodgers, ANDERSON MODEL ON A CAYLEY TREE - THE DENSITY-OF-STATES, Journal of physics. A, mathematical and general, 26(9), 1993, pp. 457-463
We describe a method of calculating the electronic density of states o
n an arbitrary tree. We use it for the problem of Anderson localizatio
n on a regular tree with random site energies and obtain the first ter
m of a weak disorder expansion of the density of states.