554 citations
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28 papers · 1 filter
A sharp threshold for a modified bootstrap percolation with recovery
Tom Coker, Karen Gunderson
Bootstrap percolation is a type of cellular automaton on graphs, introduced as a simple model of the dynamics of ferromagnetism. Vertices in a graph can be in one of two states: `h…
Random-step Markov processes
Neal Bushaw, Karen Gunderson, Steven Kalikow
We explore two notions of stationary processes. The first is called a random-step Markov process in which the stationary process of states, has a station…
Line percolation
Paul Balister, Béla Bollobás, Jonathan Lee +1
We study a new geometric bootstrap percolation model, line percolation, on the -dimensional integer grid . In line percolation with infection parameter , infection spr…
Exploring hypergraphs with martingales
Béla Bollobás, Oliver Riordan
Recently, we adapted exploration and martingale arguments of Nachmias and Peres, in turn based on ideas of Martin-Löf, Karp and Aldous, to prove asymptotic normality of the number…
The time of bootstrap percolation in two dimensions
Paul Balister, Béla Bollobás, Paul Smith
We study the distribution of the percolation time of two-neighbour bootstrap percolation on with initial set . We determine with high pr…
Bootstrap percolation on Galton-Watson trees
Béla Bollobás, Karen Gunderson, Cecilia Holmgren +2
Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number , the -neighbou…