Density of states of sparse random matrices

A supersymmetric formalism is used to derive a set of equations giving the density of states of any real, symmetric, sparse random matrix as a function of the distribution of non-zero elements and the mean number of non-zero elements per row, p. In the matrix where the non-zero elements take the values +or-1 with equal probability the equations are solved as p to infinity recovering results obtained previously with the replica method. As E to 0 the density of states rho (E) behaves as 1/E(ln(E)) 2 . The more general case where +or-1 occur with unequal probabilities is also considered.