2003/09/05 by Gunnar Pruessner, Nicholas R. Moloney · 1 citation
Engineering · Mathematics · Neuroscience · Physics and Astronomy · Psychology · #Combinatorics #Computer science #Electrical engineering #Engineering #Geology #Geometry #Markov Chains and Monte Carlo Methods #Mathematics #Neuroscience #Percolation (cognitive psychology) #Percolation threshold #Physics #Psychology #Random Matrices and Applications #Spanning tree #Statistical physics #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/36/44/003
published as J. Phys. A: Math. Gen. 36, 11213-11228 (2003) · 19 pages, 9 figures, JPA style, accepted for publication
arxiv created 2003/09/05 · openalex publication_date 2003/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using a recently developed method to simulate percolation on large clusters of distributed machines [1], we have numerically calculated crossing, spanning and wrapping probabilities in two-dimensional site and bond percolation with exceptional accuracy. Our results are fully consistent with predictions from conformal field theory. We present many new results that await theoretical explanation, particularly for wrapping clusters on a cylinder. We therefore provide possibly the most up-to-date reference for theoreticians working on crossing, spanning and wrapping probabilities in two-dimensional percolation.