Mixed Percolation Model

A mixed percolation model is a discrete percolation model such that both graph vertices and graph edges may be "blocked" from allowing fluid flow (i.e., closed in the sense of percolation theory). This is in contrast to the more-studied cases of bond percolation and site percolation, the standard models for which allow only edges and vertices, respectively, to be blocked.

Considered a bridge between bond percolation and site percolation (Chayes and Schonmann 2000), mixed percolation models have become increasingly more studied since their inception in the early 1980s. Indeed, many of the properties of and methods related to this type of percolation can be found in work done by Hammersley (1980).

Some authors extend the above definition so as to allow for the faces of the underlying graph to also be viewed as random elements to which one can assign values of open and closed (Wierman 1984). Among such models, one assigns to each planar graph the sets , , and representing the vertices, edges, and faces of , respectively, and assigns to each vertex , each edge , and each face the openness probabilities , , and , respectively. Much of the literature on such models focuses on the case in which the graph in question is a square point lattice.