Extreme paths in oriented two-dimensional percolation

E. D. Andjel, L. F. Gray

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A useful result about leftmost and rightmost paths in two-dimensional bond percolation is proved. This result was introduced without proof in Gray (1991) in the context of the contact process in continuous time. As discussed here, it also holds for several related models, including the discrete-time contact process and two-dimensional site percolation. Among the consequences are a natural monotonicity in the probability of percolation between different sites and a somewhat counter-intuitive correlation inequality.

Original languageEnglish (US)
Pages (from-to)369-380
Number of pages12
JournalJournal of Applied Probability
Issue number2
StatePublished - Jun 2016

Bibliographical note

Funding Information:
We thank the anonymous referee for a careful reading and helpful comments. This paper was written while the first author was visiting IMPA and was supported first by CAPES (grant number 1331/11-6) and then by CNPq (grant number 300722/2013-3).

Publisher Copyright:
© Applied Probability Trust 2016.


  • Extreme paths
  • Inequalities
  • Oriented percolation


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