Lower bounds for bootstrap percolation on Galton–Watson trees

Abstract

Bootstrap percolation is a cellular automaton modelling the spread of an ‘infection’ on a graph. In this note, we prove a family of lower bounds on the critical probability for r-neighbour bootstrap percolation on Galton–Watson trees in terms of moments of the offspring distributions. With this result we confirm a conjecture of Bollobás, Gunderson, Holmgren… (More)

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Cite this paper

@inproceedings{Gunderson2014LowerBF, title={Lower bounds for bootstrap percolation on Galton–Watson trees}, author={Karen Gunderson and Michał Przykucki}, year={2014} }