# Crossing estimates from metric graph and discrete GFF.

@article{Ding2020CrossingEF, title={Crossing estimates from metric graph and discrete GFF.}, author={Jian Ding and Mateo Wirth and Hao Wu}, journal={arXiv: Probability}, year={2020} }

We compare level-set percolation for Gaussian free fields (GFFs) defined on a rectangular subset of $\delta \mathbb{Z}^2$ to level-set percolation for GFFs defined on the corresponding metric graph as the mesh size $\delta$ goes to 0. In particular, we look at the probability that there is a path that crosses the rectangle in the horizontal direction on which the field is positive. We show this probability is strictly larger in the discrete graph. In the metric graph case, we show that for… CONTINUE READING

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