TY - JOUR
T1 - Lower bounds for bootstrap percolation on Galton-Watson trees
AU - Gunderson, K.
AU - Przykucki, M.
PY - 2014/7/12
Y1 - 2014/7/12
N2 - 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.
AB - 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.
KW - bootstrap percolation
KW - Galton–Watson trees
UR - https://www.scopus.com/pages/publications/84904367167
UR - https://www.scopus.com/pages/publications/84904367167
U2 - 10.1214/ECP.v19-3315
DO - 10.1214/ECP.v19-3315
M3 - Article
SN - 1083-589X
VL - 19
SP - 1
EP - 7
JO - Electronic Communications in Probability
JF - Electronic Communications in Probability
ER -