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

Jian Ding; Mateo Wirth

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arXiv · 1807.11117

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

Jian Ding·Mateo Wirth

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Abstract

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. In three dimensions and higher, we provide rather sharp estimates of percolation probabilities in different regimes which altogether describe a sharp phase transition.

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Jian Ding, Mateo Wirth. 2018-07-29. Percolation for level-sets of Gaussian free fields on metric graphs. https://arxiv.org/abs/1807.11117

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