In this talk we will look at a classical family of hierarchical lattices, with focus on its fine percolative properties. Thanks to the self-similarity of the graphs, one can establish several properties of the model, including: critical exponents, scaling relations and noise sensitivity. The results obtained are very sharp and the proofs employ a combination of tools from probability and dynamical systems.
This talk is based on a joint work with Alves, Baldasso and Moreira.