Exceptional times of the critical dynamical Erdős-Rényi graph

In this paper we introduce a network model which evolves in time, and study its largest connected component. We consider a process of graphs (G_t : t∈[0,1]), where initially we start with a critical Erdös-Rényi graph ER(n, 1/n), and then evolve forwards in time by resampling each edge independently at rate 1. We show that the size of the largest connected component that appears during the time interval [0,1] is of order n^{2/3}log^{1/3}n with high probability. This is in contrast to the largest component in the static critical Erdös-Rényi graph, which is of order n^{2/3}.