Mixed percolation models provide a bridge between bond percolation and site percolation (Chayes
and Schonmann 2000). Hammersley (1980) studied mixed Bernoulli percolation in which
the states of vertices and edges
are mutually independent, with each vertex and edge open or
closed.
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 fixes a planar graph embedding of a
planar graph and assigns to it 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. Wierman (1984) studied such models
on the square point lattice.
Chayes, L. and Schonmann, R. H. "Mixed Percolation as a Bridge between Site and Bond Percolation." Ann. Appl. Probab.10,
1182-1196, 2000.Grimmett, G. Percolation,
2nd ed. Berlin, Germany: Springer-Verlag, 1999.Hammersley, J. M.
"A Generalization of McDiarmid's Theorem for Mixed Bernoulli Percolation."
Math. Proc. Camb. Phil. Soc.88, 167-170, 1980. https://doi.org/10.1017/S0305004100057455.Wierman,
J. C. "Mixed Percolation on the Square Lattice." J. Appl. Probab.21,
247-259, 1984. https://doi.org/10.2307/3213637.
and assigns to it 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. Wierman (1984) studied such models
on the square point lattice.
