Abstract
An upper bound for the critical probability of the range-R bond percolation in and is obtained by connecting the bond percolation with the SIR epidemic model, thus complementing the lower bound result in Frei and Perkins (Electron. J. Probab. 21 (2016) Paper No. 56, 1–22).
Une borne supérieure pour la probabilité critique de la percolation par arêtes de portée R dans et est obtenue en connectant le modèle de percolation avec le modèle épidémique SIR, complétant ainsi le résultat dans Frei et Perkins (Electron. J. Probab. 21 (2016) Paper No. 56, 1–22) qui donne une borne inférieure.
Acknowledgements
This work was done as part of the author’s graduate studies at the University of British Columbia. I would like to thank my advisor, Professor Edwin Perkins, for suggesting this problem and for the helpful discussions throughout this work, especially during the global pandemic. We also thank the anonymous referee for a careful reading of the draft and for making several suggestions that improve the presentation of the paper.
Citation
Jieliang Hong. "An upper bound for in range-R bond percolation in two and three dimensions." Ann. Inst. H. Poincaré Probab. Statist. 59 (3) 1259 - 1341, August 2023. https://doi.org/10.1214/22-AIHP1305
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