Bond Percolation on the Square Lattice with Columnar Inhomogeneities

We study bond percolation on the square lattice with columnar inhomogeneities introduced in the following way: Select vertical columns at random independently with a given positive probability. Keep (resp. remove) vertical edges in the selected columns, with probability p, (resp. 1-p). All the horizontal edges and all the vertical edges lying in unselected columns are kept (resp. removed) with probability q, (resp. 1-q). We show that, if p is strictly larger than p_c (the critical point for homogeneous Bernoulli bond percolation) then q can be taken strictly smaller then p_c in such a way that the probability that the origin percolates is still positive. (Joint work with Hugo Duminil-Copin, Gady Kozma and Vladas Sidoravicius)

 

Marcelo R. Hilário is a professor at UFMG in Belo Horizonte, Brazil. He received his PHd in mathematics in 2011 at IMPA, in Rio de Janeiro, Brazil and was a visiting fellow in the Mathematical Physics group at University of Geneva in Switzerland from 2014 to 2015. His current research interests are topics in random media, mainly percolation theory and random walks in dynamical environments.