61 citations · 110 across the 13 of their papers we have counts for
4 papers · 1 filter
The time of bootstrap percolation with dense initial sets for all thresholds
Béla Bollobás, Paul Smith, Andrew J. Uzzell
We study the percolation time of the -neighbour bootstrap percolation model on the discrete torus . For at most a polylog function of and initial infection p…
The time of bootstrap percolation for dense initial sets
Béla Bollobás, Cecilia Holmgren, Paul Smith +1
In r-neighbour bootstrap percolation on the vertex set of a graph G, vertices are initially infected independently with some probability p. At each time step, the infected set expa…
Monotone cellular automata in a random environment
Béla Bollobás, Paul Smith, Andrew Uzzell
In this paper we study in complete generality the family of two-state, deterministic, monotone, local, homogeneous cellular automata in with random initial configura…
An Improved Upper Bound for Bootstrap Percolation in All Dimensions
Andrew J. Uzzell
In -neighbor bootstrap percolation on the vertex set of a graph , a set of initially infected vertices spreads by infecting, at each time step, all uninfected vertices wi…