Universality in bootstrap percolation and kinetically constrained models
Ivailo Hartarsky (Université Paris-Dauphine)

The paradigmatic 2-neighbour bootstrap percolation model is the following cellular automaton. Given a set of infected sites in Z^d, we iteratively infect each site with at least two infected neighbours, while infections never heal. We are then interested in whether and when the origin becomes infected under this dynamics starting from an i.i.d. Bernoulli initial infection. There is a naturally associated stochastic non-monotone model: the Fredrickson-Andersen 2-spin facilitated one, in which the state of each site is resampled to a Bernoulli variable at rate 1, provided it has at least 2 infected neighbours. Of course, many related models have been considered, replacing the 2-neighbour constraint by an increasing local translation-invariant constraint (e.g. both the North and East neighbours are infected). In this talk we will overview recent universality results for this class of bootstrap percolation and its non-monotone stochastic counterpart called kinetically constrained models. The outcome is a classification of all rules in terms of the scaling of the infection time of the origin when the density of infections approaches a possibly degenerate critical value.