2 research outputs found

    A large deviation approach to super-critical bootstrap percolation on the random graph Gn,pG_{n,p}

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    We consider the Erd\"{o}s--R\'{e}nyi random graph Gn,pG_{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 An∗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−An∗f(n)}n≥1\{\frac{n- A_n^*}{f(n)}\}_{n\geq 1} with explicit rate functions and allowing the scaling function ff to vary in the widest possible range.Comment: 44 page
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