ON THE LARGEST COMPONENT OF THE CRITICAL RANDOM DIGRAPH

We consider the largest component of the random digraph D(n, p) inside the critical window p = n(-1) + lambda n(-4/3). We show that the largest component C-1 has size of order n(1/3) in this range. In particular we give explicit bounds on the probabilities that vertical bar C-1 vertical bar n(-1/3) is very large or very small that are analogous to those given by Nachmias and Peres for G(n, p).