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Lower bounds for bootstrap percolation on Galton-Watson trees

   
@article{ECP3315,
	author = {Karen Gunderson and Michal Przykucki},
	title = {Lower bounds for bootstrap percolation on Galton-Watson trees},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {bootstrap percolation; 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 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, Janson and Przykucki. We also show that these bounds are best possible up to positive constants not depending on the offspring distribution.},
	pages = {no. 42, 1-7},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-3315},    
        url = {http://ecp.ejpecp.org/article/view/3315}}