105 citations · 304 across the 45 of their papers we have counts for
14 papers · 1 filter
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 second term for two-neighbour bootstrap percolation in two dimensions
Ivailo Hartarsky, Robert Morris
In the -neighbour bootstrap process on a graph , vertices are infected (in each time step) if they have at least already-infected neighbours. Motivated by its close conne…
Universality results for kinetically constrained spin models in two dimensions
Fabio Martinelli, Robert Morris, Cristina Toninelli
Kinetically constrained models (KCM) are reversible interacting particle systems on with continuous time Markov dynamics of Glauber type, which represent a natural st…
Competition in growth and urns
Daniel Ahlberg, Simon Griffiths, Svante Janson +1
We study survival among two competing types in two settings: a planar growth model related to two-neighbour bootstrap percolation, and a system of urns with graph-based interaction…