Universal Behavior for Bond Percolation
Eric I. Corwin, Robin Stinchcombe, M.F. Thorpe
TL;DR
This paper reviews bond percolation across multiple lattice types and dimensions, demonstrating how properties converge to Erdős-Rényi graph behavior in high dimensions, with new results on hyper-sphere packings up to nine dimensions.
Contribution
It provides a comprehensive collection of bond percolation results across various lattices and dimensions, including new findings on hyper-sphere packings up to nine dimensions.
Findings
Mean coordination approaches Erdős-Rényi limit in high dimensions
Excess kurtosis and skewness evolve smoothly with dimension
New results on bond diluted hyper-sphere packs in up to nine dimensions
Abstract
We collect together results for bond percolation on various lattices from two to fourteen dimensions which, in the limit of large dimension or number of neighbors , smoothly approach a randomly diluted Erd\H{o}s-R\'enyi graph. We include new results on bond diluted hyper-sphere packs in up to nine dimensions, which show the mean coordination, excess kurtosis and skewness evolving smoothly with dimension towards the Erd\H{o}s-R\'enyi limit.
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