Poisson convergence and Poisson processes with applications to random graphs (Q1096252)

The author uses the Stein-Chen method to establish conditions under which a sequence of sums of dependent indicator random variables converges in distribution to a Poisson limit. The result is then extended to provide new sufficient conditions for the convergence of weakly dependent point processes to a Poisson point process. The theorems are applied to a variety of attractive problems from random graph theory, including that of finding the approximate distribution of the size of the first cycle in a graph with a large number of vertices, when edges are added one by one at random.