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Lower bounds for bootstrap percolation on Galton-Watson trees


 
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1. Title Title of document Lower bounds for bootstrap percolation on Galton-Watson trees
 
2. Creator Author's name, affiliation, country Karen Gunderson; Heilbronn Institute, University of Bristol; United Kingdom
 
2. Creator Author's name, affiliation, country Michal Przykucki; University of Cambridge and London Institute for Mathematical Sciences; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) bootstrap percolation; Galton-Watson trees
 
3. Subject Subject classification 05C05; 60K35; 60C05; 60J80; 05C80
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) M. Przykucki supported in part by MULTIPLEX no. 317532.
 
7. Date (YYYY-MM-DD) 2014-07-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/3315
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3315
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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