  We revisit the derivation of the density of states of sparse random matrices.
We derive a recursion relation that allows one to compute the spectrum of the
matrix of incidence for finite trees that determines completely the low
concentration limit. Using the iterative scheme introduced by Biroli and
Monasson [J. Phys. A 32, L255 (1999)] we find an approximate expression for the
density of states expected to hold exactly in the opposite limit of large but
finite concentration. The combination of the two methods yields a very simple
simple geometric interpretation of the tails of the spectrum. We test the
analytic results with numerical simulations and we suggest an indirect
numerical method to explore the tails of the spectrum.
