  Cluster concepts have been extremely useful in elucidating many problems in
physics. Percolation theory provides a generic framework to study the behavior
of the cluster distribution. In most cases the theory predicts a geometrical
transition at the percolation threshold, characterized in the percolative phase
by the presence of a spanning cluster, which becomes infinite in the
thermodynamic limit. Standard percolation usually deals with the problem when
the constitutive elements of the clusters are randomly distributed. However
correlations cannot always be neglected. In this case correlated percolation is
the appropriate theory to study such systems. The origin of correlated
percolation could be dated back to 1937 when Mayer [1] proposed a theory to
describe the condensation from a gas to a liquid in terms of mathematical
clusters (for a review of cluster theory in simple fluids see [2]). The
location for the divergence of the size of these clusters was interpreted as
the condensation transition from a gas to a liquid. One of the major drawback
of the theory was that the cluster number for some values of thermodynamic
parameters could become negative. As a consequence the clusters did not have
any physical interpretation [3]. This theory was followed by Frenkel's
phenomenological model [4], in which the fluid was considered as made of non
interacting physical clusters with a given free energy. This model was later
improved by Fisher [3], who proposed a different free energy for the clusters,
now called droplets, and consequently a different scaling form for the droplet
size distribution. This distribution, which depends on two geometrical
parameters, has the nice feature that the mean droplet size exhibits a
divergence at the liquid-gas critical point.
