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 ${\mu }^2$→∞. Applications to the theory of ‘‘Griffiths singularities’’ in dilute magnets are discussed.