Lower bounds for bootstrap percolation on Galton-Watson trees

Karen Gunderson*, Michal Przykucki

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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 Bollobas, Gunderson, Holmgren, Janson and Przykucki. We also show that these bounds are best possible up to positive constants not depending on the offspring distribution.

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalElectronic Communications in Probability
Volume19
DOIs
Publication statusPublished - 12 Jul 2014

Keywords

  • bootstrap percolation
  • Galton-Watson trees

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