Abstract
We prove the uniqueness of the infinite connected component for the vacant set of random interlacements on general vertex-transitive amenable transient graphs. Our approach is based on connectedness of random interlacements and differs from the one used by Teixera [10] to prove the uniqueness of the infinite connected component for the vacant set of random interlacements on .
Funding Statement
The research of both authors has been supported by the DFG Priority Program 2265 “Random Geometric Systems” (Project number 443849139).
Citation
Yingxin Mu. Artem Sapozhnikov. "Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs." Electron. Commun. Probab. 28 1 - 9, 2023. https://doi.org/10.1214/23-ECP564
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