Intuitively, a model of -dimensional percolation
theory is said to be a Bernoulli model if the open/closed status of an area is
completely random. In particular, it makes sense to talk about a Bernoulli bond percolation,
Bernoulli site percolation, as well as describing other models of both discrete
and continuum percolation theory as
being Bernoulli.
Due to the vastness of the literature on percolation theory, however, there is a certain lack of uniformity in its terminology; as such, some authors choose to define
-dimensional
Bernoulli percolation strictly in terms of its behavior on the standard bond percolation
model within the regular point lattice. According to this view, the term Bernoulli percolation
refers to the independent assignment as either
open (with probability ) or closed (with probability ) to each edge where here,
This perspective, though framed relative to obvious graph theory terminology, is largely probabilistic (Cerf 2006).
-dimensional percolation
theory is said to be a Bernoulli model if the open/closed status of an area is
completely random. In particular, it makes sense to talk about a Bernoulli bond percolation,
Bernoulli site percolation, as well as describing other models of both discrete
and continuum percolation theory as
being Bernoulli.
-dimensional
Bernoulli percolation strictly in terms of its behavior on the standard bond percolation
model within the regular point lattice 
. According to this view, the term Bernoulli percolation
refers to the independent assignment as either
open (with probability ![p in [0,1]](/images/equations/BernoulliPercolationModel/Inline4.svg)
) or closed (with probability 
) to each edge 
where here,
