A large deviation approach to super-critical bootstrap percolation on the random graph G_n,p

02/06/2018

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by   Giovanni Luca Torrisi, et al.

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We consider the Erdös--Rényi random graph G_n,p and we analyze the simple irreversible epidemic process on the graph, known in the literature as bootstrap percolation. We give a quantitative version of some results by Janson et al. (2012), providing a fine asymptotic analysis of the final size A_n^* of active nodes, under a suitable super-critical regime. More specifically, we establish large deviation principles for the sequence of random variables {n- A_n^*/f(n)}_n≥ 1 with explicit rate functions and allowing the scaling function f to vary in the widest possible range.