(Department of Mathematics, University of Manitoba)
|Date||Friday, February 16, 2018|
Given a graph G and a positive integer r, the r-neighbor bootstrap percolation process on G is defined in the following way: A subset A of vertices is initially infected, and any vertex outside A is healthy. We then successively infect each healthy vertex that has at least r infected neighbours. If every vertex is eventually infected, say that A percolates.
Bootstrap percolation has been the subject of much study in both the probabilistic and deterministic models, in particular on the grid. The maximum time to percolation in the grid has been determined precisely and in this talk, I will present some new results on how quickly a 'small’ initial configuration can percolate.
This talk is based on joint work with Stefan David.