Consider activating the $n$ vertices of a discrete square torus one at a time in uniformly random order. For $n$ large, when does an active 3-core (subgraph with minimum degree at least 3 induced by active vertices) appear and what is its size when it does? We answer these questions, revealing a somewhat surprising explosion, stronger than the mean-field phenomenology, covered by the classical work of Łuczak. The tools involved in the proof come from well-established bootstrap percolation theory. Yet, extending the result to other lattices is much more challenging and is the main focus of our work. This talk is based primarily on joint work with Lyuben Lichev available at https://arxiv.org/abs/2501.18976, but also related joint works with Hugo Duminil-Copin and with Augusto Teixeira.
