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2014 Lower bounds for bootstrap percolation on Galton-Watson trees
Karen Gunderson, Michal Przykucki
Author Affiliations +
Electron. Commun. Probab. 19: 1-7 (2014). DOI: 10.1214/ECP.v19-3315

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.

Citation

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Karen Gunderson. Michal Przykucki. "Lower bounds for bootstrap percolation on Galton-Watson trees." Electron. Commun. Probab. 19 1 - 7, 2014. https://doi.org/10.1214/ECP.v19-3315

Information

Accepted: 12 July 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1298.05064
MathSciNet: MR3233204
Digital Object Identifier: 10.1214/ECP.v19-3315

Subjects:
Primary: 05C05
Secondary: 05C80, 60C05, 60J80, 60K35

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