Anisotropic Percolation on Slabs

2013/09/04 by Rodrigo G. Couto, Couto, Rodrigo G., Bernardo N. B. de Lima +3
Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1309.1118

7 pages

arxiv created 2013/09/04 · openalex publication_date 2013/09/04 · arxiv updated 2013/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider anisotropic independent bond percolation models on the slab \Z²×\0,…,k\, where we suppose that the axial (vertical) bonds are open with probability p, while the radial (horizontal) bonds are open with probability q. We study the critical curves for these models and establish their continuity and strict monotonicity.

Related

• Critical percolation on slabs with random columnar disorder
• Critical scaling for an anisotropic percolation system on ℤ²
• Monotonicity of the critical point in two-dimensional oriented percolation with enhancement
• Invariant splitting of a slab into infinitely many robust clusters
• A note on the phase transition for independent alignment percolation