61 citations · 83 across the 11 of their papers we have counts for
14 papers
Subcritical monotone cellular automata
Paul Balister, Béla Bollobás, Robert Morris +1
We study monotone cellular automata (also known as -bootstrap percolation) in with random initial configurations. Confirming a conjecture of Balister, B…
The critical length for growing a droplet
Paul Balister, Béla Bollobás, Robert Morris +1
In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the cr…
Universality for monotone cellular automata
Paul Balister, Béla Bollobás, Robert Morris +1
In this paper we study monotone cellular automata in dimensions. We develop a general method for bounding the growth of the infected set when the initial configuration is chose…
The sharp threshold for the Duarte model
Béla Bollobás, Hugo Duminil-Copin, Robert Morris +1
The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollobás, Smith and Uzzell, and the critical threshold for percolation was determine…
Nucleation and growth in two dimensions
Béla Bollobás, Simon Griffiths, Robert Morris +2
We consider a dynamical process on a graph , in which vertices are infected (randomly) at a rate which depends on the number of their neighbours that are already infected. This…
The threshold for jigsaw percolation on random graphs
Béla Bollobás, Oliver Riordan, Erik Slivken +1
Jigsaw percolation is a model for the process of solving puzzles within a social network, which was recently proposed by Brummitt, Chatterjee, Dey and Sivakoff. In the model there…