Inhomogeneous percolation on ladder graphs

2019. 05. 09. 16:15
Réka Szabó (Groningen)

We define an inhomogeneous percolation model on `ladder graphs'  obtained as direct products of an arbitrary graph G = (V,E) and the set of integers (vertices are thought of as having a `vertical' component indexed by an integer). We make two natural choices for the set of edges, producing an non-oriented and an oriented graph. These graphs are endowed with percolation configurations in which independently, edges inside a fixed infinite `column' are open with probability q, and all other edges are open with probability p. For all fixed q one can define the critical percolation threshold p_c(q). We show that this function is continuous in (0, 1). Join work with D. Valesin.