16/02/2022, 16:00 — 17:00 — Online
Marcelo Hilario, Universidade Federal de Minas Gerais
Percolation on the cubic lattice with lower dimensional disorder
Percolation on the Euclidean d-dimensional lattice has been studied for over sixty years and is still a fascinating source of interesting mathematical problems. The fact that this model undergoes a non-trivial phase transition is well-understood since the early studies in the Bernoulli setting, where the lattice is regular and there are no inhomogeneities on the parameters. One way to introduce random disorder is, for example, either passing to a dilute lattice where lower dimensional affine hyperplanes are removed or, alternately, introducing inhomogeneities on the parameter along such hyperplanes. In these situations, even to establish that non-trivial phase transition takes place may be a hard task. In this talk we review some recent results on this topic and discuss some open problems.
