105 citations · 718 across the 103 of their papers we have counts for
5 papers · 1 filter
The sharp threshold for bootstrap percolation in all dimensions
József Balogh, Béla Bollobás, Hugo Duminil-Copin +1
In r-neighbour bootstrap percolation on a graph G, a (typically random) set A of initially 'infected' vertices spreads by infecting (at each time step) vertices with at least r alr…
Bootstrap percolation in high dimensions
Jozsef Balogh, Bela Bollobas, Robert Morris
In r-neighbour bootstrap percolation on a graph G, a set of initially infected vertices A \subset V(G) is chosen independently at random, with density p, and new vertices are subse…
Hamilton cycles in random geometric graphs
József Balogh, Béla Bollobás, Michael Krivelevich +2
We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penro…
The Klee-Minty random edge chain moves with linear speed
Jozsef Balogh, Robin Pemantle
An infinite sequence of 0's and 1's evolves by flipping each~1 to a~0 exponentially at rate one. When a~1 flips, all bits to its right also flip. Starting from any configuration wi…
Bootstrap percolation on infinite trees and non-amenable groups
Jozsef Balogh, Yuval Peres, Gabor Pete
Bootstrap percolation on an arbitrary graph has a random initial configuration, where each vertex is occupied with probability p, independently of each other, and a deterministic s…