2 research outputs found
A large deviation approach to super-critical bootstrap percolation on the random graph
We consider the Erd\"{o}s--R\'{e}nyi random graph 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
of active nodes, under a suitable super-critical regime. More
specifically, we establish large deviation principles for the sequence of
random variables with explicit rate
functions and allowing the scaling function to vary in the widest possible
range.Comment: 44 page