Universality in bootstrap percolation and kinetically constrained models

The paradigmatic 2-neighbour bootstrap percolation model is the following cellular automaton. Given a set of infected sites in Z^2, we iteratively infect each site with at least 2 infected neighbours, while infections never heal. We are then interested 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 (desired) 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.