A large deviation approach to super-critical bootstrap percolation on the random graph G(n,p)

We consider the Erdös-Rényi random graph G(n,p) and we analyze the simple irreversible epidemicprocess on the graph, known in the literature as bootstrap percolation. We give a quantitative version ofsome results by Janson et al. (2012), providing a fine asymptotic analysis of the final size A_n of activenodes, under a suitable super-critical regime. More specifically, we establish large deviation principles forthe sequence of random variables n-A_n/f (n) with explicit rate functions and allowing the scaling functionf to vary in the widest possible range.