Density of states of a sparse random matrix

The density of states {ρ}({μ}) of an N×{}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 μ²{→}{∞}. Applications to the theory of ``Griffiths singularities'' in dilute magnets are discussed.