Abstract: In the first half of the talk, we consider a generalised oriented site percolation process on 
(GOSP). We introduce a renormalisation construction and show how it can be used to obtain some results about the shape of the infinite cluster in the supercritical regime.
In the second part we discuss bootstrap percolation models of the so-called “subcritical” type (this has nothing to do with the usual notion of subcritical phase). While progressively elucidating their relation to GOSP, we emphasise why the subject could interest percolation specialists.
For both models we work in two dimensions, though most of the treatment is valid in any dimension. The two parts are based on https://arxiv.org/abs/2103.15621 and https://arxiv.org/abs/1806.11405 respectively.