Abstract
In this short note, we show that the critical threshold for the percolation of metric graph loop soup on a large class of transient metric graphs (including quasi-transitive graphs such as , ) is .
Funding Statement
The authors acknowledge the support of National Key R&D Program of China (No. 2021YFA1002700 and No. 2020YFA0712900). YC acknowledges the support of NSFC (No. 11701395). HD is partially supported by the elite undergraduate training program of School of Mathematical Science at Peking University. XL acknowledges the support of NSFC (No. 12071012).
Acknowledgments
We thank two anonymous referees for their helpful and detailed comments on an earlier version of the manuscript. XL also wishes to thank Pierre-Francois Rodriguez, Alex Drewitz and Zhenhao Cai for various helpful discussions.
Citation
Yinshan Chang. Hang Du. Xinyi Li. "Percolation threshold for metric graph loop soup." Bernoulli 30 (4) 3324 - 3333, November 2024. https://doi.org/10.3150/23-BEJ1716
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