Open Access
2009 Some two-dimensional finite energy percolation processes
Olle Häggström, Péter Mester
Author Affiliations +
Electron. Commun. Probab. 14: 42-54 (2009). DOI: 10.1214/ECP.v14-1446


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.


Download Citation

Olle Häggström. Péter Mester. "Some two-dimensional finite energy percolation processes." Electron. Commun. Probab. 14 42 - 54, 2009.


Accepted: 4 February 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60176
MathSciNet: MR2481665
Digital Object Identifier: 10.1214/ECP.v14-1446

Primary: 60K35

Keywords: Coexistence , percolation , uniform finite energy

Back to Top