50:36
published on February 6, 2026
On some deterministic version of the random walk on $\mathbb{Z}^d$
By Dalia Terhesiu
Bootstrap percolation on Erdos-Renyi graphs
By Omer Angel
Appears in collection : Dynamics on random graphs and random maps / Dynamiques sur graphes et cartes aléatoires
We consider bootstrap percolation on the Erdos-Renyi graph: given an initial infected set, a vertex becomes infected if it has at least $r$ infected neighbours. The graph is susceptible if there exists an initial set of size $r$ that infects the whole graph. We identify the critical threshold for susceptibility. We also analyse Bollobas's related graph-bootstrap percolation model. Joint with Brett Kolesnik.
