Scaling Limits of Crossing Probabilities in Metric Graph GFF

Abstract

We consider metric graph Gaussian free field (GFF) defined on polygons of $\delta {\mathbb{Z}}^2$ with alternating boundary data. The crossing probabilities for level-set percolation of metric graph GFF have scaling limits. When the boundary data is well-chosen, the scaling limits of crossing probabilities can be explicitly constructed as "fusion" of multiple SLE${}_4$ pure partition functions.

42 pages, 6 figures