Percolation in high dimensions is not understood
S. Fortunato, D. Stauffer, A. Coniglio
TL;DR
This paper investigates the behavior of percolation in high dimensions, revealing that the number of spanning clusters in four to nine dimensions deviates from expected theoretical models, indicating gaps in current understanding.
Contribution
It highlights the discrepancy between observed spanning cluster counts and theoretical predictions in high-dimensional percolation, challenging existing models.
Findings
Number of spanning clusters does not follow expected size dependence
Deviations observed in four to nine dimensions
Current models may need revision to account for these results
Abstract
The number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Bayesian Methods and Mixture Models · Random Matrices and Applications