Abstract
In this paper, we show several rigorous results on the phase transition of Finitary Random Interlacements (FRI). For the high intensity regime, we show the existence of a critical fiber length, and find its exact asymptotic as intensity goes to infinity. At the same time, our result for the low intensity regime proves the global existence of a non-trivial phase transition with respect to the system intensity.
Funding Statement
Research supported by National Key R&D Program of China, Project Number 2020YFA0712902.
Acknowledgments
The authors would like to thank an anonymous referee for helpful comments. The authors would like to thank Drs. Xinyi Li, Eviatar B. Procaccia, and Ron Rosenthal for fruitful discussions. The authors would also like to thank Dr. Eviatar B. Procaccia for allowing us to use his LaTeX macros.
Citation
Zhenhao Cai. Yuan Zhang. "Some rigorous results on the phase transition of finitary random interlacements." Electron. Commun. Probab. 26 1 - 11, 2021. https://doi.org/10.1214/21-ECP424
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