Probability Seminar “Inhomogeneous percolation with random one-dimensional reinforcements”

January 15, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)

Local: room C116 - Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online.

Speaker: Alan Bruno do Nascimento (UFMG)

Abstract: In this talk we consider inhomogeneous Bernoulli bond percolation on the graph GxZ, where G is an infinite connected graph with bounded degree and Z is the set of integers. In 1994, Madras, Schinazi and Schonman showed that there is no percolation in Z^d  if the edges  are open with a probability of q<1 if they lie on a fixed axis and with a probability of p<p_c(Z^d) otherwise. Here, we consider a region given by boxes with iid radii centered along the vertical axis 0xZ of GxZ. We allow each edge to be open with a probability of q<1 if it is inside this region and with a probability of p<p_c(GxZ) otherwise. The goal of the talk is to show that, even if the region is connected, occurrence or not of percolation in this inhomogeneous model depends on how sparse and how large are the boxes placed along the axis. We aim to give sufficient conditions on the moments of the radii as a function of the growth of the graph G for percolation not to occur.
This is a joint work with Rémy Sanchis and Daniel Ungaretti.

More complete information about the seminars can be found at DME

Organizers: Giulio Iacobelli e Maria Eulalia Vares