Density of states of a sparse random matrix

The density of states () of an N real, symmetric, random matrix with elements 0, 1 is calculated in the limit N as a function of the average ``connectivity'' p, i. e. , of the mean number of nonzero elements per row. For p, the Wigner semicircular distribution is recovered. For finite p the distribution has tails extending beyond the semicircle, with for ^2. Applications to the theory of ``Griffiths singularities'' in dilute magnets are discussed.