Report Number: CS-TR-82-933
Institution: Stanford University, Department of Computer Science
Title: An algorithmic method for studying percolation clusters
Author: Klein, Shmuel T.
Author: Shamir, Eli
Date: September 1982
Abstract: In percolation theory one studies configurations, based on
some infinite lattice, where the sites of the lattice are
randomly made F (full) with probability p or E (empty) with
probability 1-p. For p > $p_c$, the set of configurations
which contain an infinite cluster (a connectivity component)
has probability 1. Using an algorithmic method and a
rearrangement lemma for Bernoulli sequences, we compute the
boundary-to-body quotient of infinite clusters and prove it
has the definite value (1-p)/p with probability 1.