English

Some two-dimensional finite energy percolation processes

Probability 2010-11-15 v1

Abstract

Some examples of translation invariant site percolation processes on the Z2\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 00 and 11) 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.

Keywords

Cite

@article{arxiv.1011.2872,
  title  = {Some two-dimensional finite energy percolation processes},
  author = {Olle Hägström and Péter Mester},
  journal= {arXiv preprint arXiv:1011.2872},
  year   = {2010}
}

Comments

14 pages

R2 v1 2026-06-21T16:42:49.304Z