Percolation for level-sets of Gaussian free fields on metric graphs

Understand

We study level-set percolation for Gaussian free fields on metric graphs.

• In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus.
• Our bound holds with high probability conditioned on connectivity and the bound is sharp up to a poly-logarithmic factor with an exponent of one-quarter.
• This substantially improves a previous result by Li and the first author.