Gaussian free field on metric graphs
This page presents simulations for the phase transition associated to percolation for the level sets of the Gaussian free field on the metric graph associated to the three-dimensional square lattice. 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, random interlacements, and independent percolation.
10% largest connected components
The figures below show the level sets of the metric graph Gaussian free field above level h 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=0.3
h=0
h=-0.3
GFF_Cable_N=175_Free_Boundary_10_Percent_Largest_1.mp4
h=0.3
h=0
h=-0.3
GFF_Cable_N=200_Free_Boundary_2_Largest.mp4