Abstract
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 language | English (US) |
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Pages (from-to) | 369-380 |
Number of pages | 12 |
Journal | Journal of Applied Probability |
Volume | 53 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2016 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© Applied Probability Trust 2016.
Keywords
- Extreme paths
- Inequalities
- Oriented percolation