Some two-dimensional finite energy percolation processes
Olle Häggström, Chalmers University of Technology
Péter Mester, Indiana University
Abstract
Some examples of translation invariant site percolation processes
on the $Z^2$ lattice are constructed, the most far-reaching example being
one that satisfies uniform finite
energy (meaning that the probability that a site is open given the
status of all others is bounded away from 0 and 1) and exhibits a.s.
the coexistence of an infinite open cluster and an infinite closed cluster.
Essentially the same example shows that coexistence is possible
between an infinite open cluster and an infinite closed cluster that are
both robust under i.i.d. thinning.
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