Probability seminar: Marcelo Richard Hilario, Universidade Federal de Minas Gerais
SM3, School of Mathematics
Marcelo Richard Hilario, Universidade Federal de Minas Gerais
Some percolation processes with infinite-range dependencies
Consider the hyper-cubic lattice and remove the lines parallel to the coordinate axis independently at random. What are the properties of the set of remaining vertices? Does this model undergo a sharp phase transition as the probability of removing the lines vary? How many connected components are there? What if we remove cylinders from the Euclidian space in a isometry invariant way? In this talk we discuss some of this questions. We also discuss for Bernoulli percolation processes in the square lattice, how enhancing the parameter in a set of vertical lines chosen uniformly at random changes the critical point.