Independent Percolation
This page presents simulations for the phase transition associated to independent percolation in dimension three. The python script for these simulations is available here, along with the required companion package. You are welcome to use and modify them. Similar simulations are also available for the discrete Gaussian free field, metric graph Gaussian free field and random interlacements.
10% largest connected components
The figures below show the level sets of an independent standard Gaussian free field above level h (instead of standard Bernoulli percolation for easier comparison with the GFF) in a box with side length N for various values of N and h, corresponding respectively to the subcritical, critical, and supercritical regime. Only connected components with a cardinality exceeding 10% of the largest component are displayed. The video can be downloaded here, and a 3D representation with more points is available here (can be slow).Â
h=0.55
h=0.49
h=0.43
IID_N=200_Free_Boundary_10_Percent_Largest_1.mp4
h=0.55
h=0.49
h=0.43
IID_N=200_Free_Boundary_2_Largest_1.mp4