4 papers
Sharpness of the Phase Transition for the Orthant Model
Thomas Beekenkamp
The orthant model is a directed percolation model on , in which all clusters are infinite. We prove a sharp threshold result for this model: if is larger than the…
Sharpness of the Phase Transition for the Corrupted Compass Model on Transitive Graphs
Thomas Beekenkamp
In the corrupted compass model on a vertex-transitive graph, a neighbouring edge of every vertex is chosen uniformly at random and opened. Additionally, with probability , indep…
Sharpness of the Percolation Phase Transition for the Contact Process on
Thomas Beekenkamp
We study percolation properties of the upper invariant measure of the contact process on . Our main result is a sharp percolation phase transition with exponentially…
Sharpness for Inhomogeneous Percolation on Quasi-Transitive Graphs
Thomas Beekenkamp, Tim Hulshof
In this note we study the phase transition for percolation on quasi-transitive graphs with quasi-transitively inhomogeneous edge-retention probabilities. A quasi-transitive graph i…