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.

http://i.stanford.edu/pub/cstr/reports/cs/tr/82/933/CS-TR-82-933.pdf