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2021 Scaling limits of crossing probabilities in metric graph GFF
Mingchang Liu, Hao Wu
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Electron. J. Probab. 26: 1-46 (2021). DOI: 10.1214/21-EJP598


We consider metric graph Gaussian free field (GFF) defined on polygons of δZ2 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 SLE4 pure partition functions.

Funding Statement

Supported by Beijing Natural Science Foundation (JQ20001, Z180003) and Thousand Talents Plan for Young Professionals.


We acknowledge Jian Ding, Titus Lupu, and Mateo Wirth for helpful discussion on GFF. We acknowledge Eveliina Peltola for stimulating discussion about partition functions for multiple SLEs. We acknowledge the referee for careful comments which improved the presentation and provided deep insight into CFT.


Download Citation

Mingchang Liu. Hao Wu. "Scaling limits of crossing probabilities in metric graph GFF." Electron. J. Probab. 26 1 - 46, 2021.


Received: 21 May 2020; Accepted: 3 March 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-EJP598

Primary: 60G15 , 60G60 , 60J67

Keywords: Crossing probability , Gaussian free field , Schramm Loewner Evolution


Vol.26 • 2021
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