A central limit theorem for decomposable random variables with applications to random graphs

Abstract

The application of Stein's method of obtaining rates of convergence to the normal distribution is illustrated in the context of random graph theory. Problems which exhibit a dissociated structure and problems which do not are considered. Results are obtained for the number of copies of a given graph G in K( n, p), for the number of induced copies of G, for the number of isolated trees of order k ≥ 2, for the number of vertices of degree d ≥ 1, and for the number of isolated vertices.